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Journal articles on the topic 'Coloring graph'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Slilaty, Daniel. "Coloring permutation-gain graphs." Contributions to Discrete Mathematics 16, no. 1 (2021): 47–52. http://dx.doi.org/10.55016/ojs/cdm.v16i1.62717.

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Correspondence colorings of graphs were introduced in 2018 by Dvořák and Postle as a generalization of list colorings of graphs which generalizes ordinary graph coloring. Kim and Ozeki observed that correspondence colorings generalize various notions of signed-graph colorings which again generalizes ordinary graph colorings. In this note we state how correspondence colorings generalize Zaslavsky's notion of gain-graph colorings and then formulate a new coloring theory of permutation-gain graphs that sits between gain-graph coloring and correspondence colorings. Like Zaslavsky's gain-graph colo

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Ei, Ei Moe. "Application of Vertex Colorings with Some Interesting Graphs." International Journal of Trend in Scientific Research and Development 3, no. 6 (2019): 991–96. https://doi.org/10.5281/zenodo.3589203.

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Firstly, basic concepts of graph and vertex colorings are introduced. Then, some interesting graphs with vertex colorings are presented. A vertex coloring of graph G is an assignment of colors to the vertices of G. And then by using proper vertex coloring, some interesting graphs are described. By using some applications of vertex colorings, two problems is presented interestingly. The vertex coloring is the starting point of graph coloring. The chromatic number for some interesting graphs and some results are studied. Ei Ei Moe "Application of Vertex Colorings with Some Interesting Graph

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R. Sudhakar. "Equitable Total Coloring of Line Graph of Certain Graphs." Communications on Applied Nonlinear Analysis 32, no. 9s (2025): 2370–79. https://doi.org/10.52783/cana.v32.4524.

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An equitable total-coloring of a graph G is a proper total-coloring such that the number of vertices and edges in any two color classes differ by at most one. In this paper, we determined the equitable total chromatic number for line graph of ladder, slanting ladder, triangular snake, alternate triangular snake, quadrilateral snake and alternate quadrilateral snake Introduction: Graph coloring is a fundamental problem in graph theory with applications in scheduling, networking, and resource allocation. A total-coloring of a graph G is an assignment of colors to both vertices and edges such tha

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Prajnanaswaroopa, Shantharam, Jayabalan Geetha, Kanagasabapathi Somasundaram, and Teerapong Suksumran. "Total Coloring of Some Classes of Cayley Graphs on Non-Abelian Groups." Symmetry 14, no. 10 (2022): 2173. http://dx.doi.org/10.3390/sym14102173.

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Total Coloring of a graph G is a type of graph coloring in which any two adjacent vertices, an edge, and its incident vertices or any two adjacent edges do not receive the same color. The minimum number of colors required for the total coloring of a graph is called the total chromatic number of the graph, denoted by χ″(G). Mehdi Behzad and Vadim Vizing simultaneously worked on the total colorings and proposed the Total Coloring Conjecture (TCC). The conjecture states that the maximum number of colors required in a total coloring is Δ(G)+2, where Δ(G) is the maximum degree of the graph G. Graph

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Rupam, Shrivastava, and Dr. Satish Agnihotri Prof. "A Study on the Total Coloring and Equitable Total Coloring for Splitting Graph." International Journal of Contemporary Research in Multidisciplinary 3, no. 5 (2024): 137–42. https://doi.org/10.5281/zenodo.13862782.

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This study focuses on the total coloring and equitable total coloring of splitting graphs, an area of graph theory that examines the assignment of colors to both vertices and edges under specific constraints. Total coloring involves assigning distinct colors to adjacent or incident elements (vertices and edges) in such a way that no two adjacent or incident elements share the same color. Equitable total coloring further requires the distribution of colors across vertices and edges to be as balanced as possible. The splitting graph, derived from a base graph by splitting its vertices, presents

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Bagheri Gh., Behrooz, and Behnaz Omoomi. "On the simultaneous edge coloring of graphs." Discrete Mathematics, Algorithms and Applications 06, no. 04 (2014): 1450049. http://dx.doi.org/10.1142/s1793830914500499.

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A μ-simultaneous edge coloring of graph G is a set of μ proper edge colorings of G with a same color set such that for each vertex, the sets of colors appearing on the edges incident to that vertex are the same in each coloring and no edge receives the same color in any two colorings. The μ-simultaneous edge coloring of bipartite graphs has a close relation with μ-way Latin trades. Mahdian et al. (2000) conjectured that every bridgeless bipartite graph is 2-simultaneous edge colorable. Luo et al. (2004) showed that every bipartite graphic sequence S with all its elements greater than one, has

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Erzurumluoğlu, Aras, and C. A. Rodger. "On Evenly-Equitable, Balanced Edge-Colorings and Related Notions." International Journal of Combinatorics 2015 (March 4, 2015): 1–7. http://dx.doi.org/10.1155/2015/201427.

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A graph G is said to be even if all vertices of G have even degree. Given a k-edge-coloring of a graph G, for each color i∈Zk={0,1,…,k-1} let G(i) denote the spanning subgraph of G in which the edge-set contains precisely the edges colored i. A k-edge-coloring of G is said to be an even k-edge-coloring if for each color i∈Zk, G(i) is an even graph. A k-edge-coloring of G is said to be evenly-equitable if for each color i∈Zk, G(i) is an even graph, and for each vertex v∈V(G) and for any pair of colors i,j∈Zk, |degG(i)(v)-degG(j)(v)|∈{0,2}. For any pair of vertices {v,w} let mG({v,w}) be the num

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Abhishek, Kumar. "Strongly set-colorable graphs." Discrete Mathematics, Algorithms and Applications 11, no. 01 (2019): 1950007. http://dx.doi.org/10.1142/s1793830919500071.

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In [S. M. Hegde, Set colorings of graphs, European J. Combin. 30 (2009) 986–995.] Hegde introduced the notion of set colorings of a graph [Formula: see text] as an assignment of distinct subsets of a finite set [Formula: see text] of [Formula: see text] colors to the vertices of [Formula: see text] such that all the colors of the edges which are obtained as the symmetric differences of the subsets assigned to their end-vertices are distinct. Additionally, if all the sets on the vertices and edges of [Formula: see text] are the set of all nonempty subsets of [Formula: see text] then the colorin

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Nuroeni, Ilmiatun, Arika Indah Kristiana, Saddam Hussen, Susi Setiawani, and Robiatul Adawiyah. "LOCAL IRREGULARITY POINT COLORING ON THE RESULT OF SUBDIVISION OPERATION OF HELM GRAPHS." Jurnal Diferensial 5, no. 2 (2023): 117–25. http://dx.doi.org/10.35508/jd.v5i2.12197.

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One of the sub-chapters studied in graphs is local irregularity vertex coloring of graph. The based on definition of local irregularity vertex coloring of graph, as follow : (i)l : V (G) →{1, 2, 3, . . . , k} as a vertex irregular labeling and w : V (G) → N, for every uv ∈ E(G), w(u) ̸=w(v) with w(u) = Pv∈N(u)l(v) and (i) Opt(l) = min{max(li); li is a vertex irregular labeling}. The chromatic number of the local irregularity vertex coloring of G denoted by χlis(G), is the minimum cardinality of the largest label over all such local irregularity vertex colorings. In this article, discuss about

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Ma, Baolin, and Chao Yang. "Distinguishing colorings of graphs and their subgraphs." AIMS Mathematics 8, no. 11 (2023): 26561–73. http://dx.doi.org/10.3934/math.20231357.

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<abstract><p>In this paper, several distinguishing colorings of graphs are studied, such as vertex distinguishing proper edge coloring, adjacent vertex distinguishing proper edge coloring, vertex distinguishing proper total coloring, adjacent vertex distinguishing proper total coloring. Finally, some related chromatic numbers are determined, especially the comparison of the correlation chromatic numbers between the original graph and the subgraphs are obtained.</p></abstract>

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Li, Minhui, Shumin Zhang, Caiyun Wang, and Chengfu Ye. "The Dominator Edge Coloring of Graphs." Mathematical Problems in Engineering 2021 (October 7, 2021): 1–7. http://dx.doi.org/10.1155/2021/8178992.

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Let G be a simple graph. A dominator edge coloring (DE-coloring) of G is a proper edge coloring in which each edge of G is adjacent to every edge of some color class (possibly its own class). The dominator edge chromatic number (DEC-number) of G is the minimum number of color classes among all dominator edge colorings of G , denoted by χ d ′ G . In this paper, we establish the bounds of the DEC-number of a graph, present the DEC-number of special graphs, and study the relationship of the DEC-number between G and the operations of G .

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Dobrinen, Natasha. "The Ramsey theory of the universal homogeneous triangle-free graph." Journal of Mathematical Logic 20, no. 02 (2020): 2050012. http://dx.doi.org/10.1142/s0219061320500129.

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The universal homogeneous triangle-free graph, constructed by Henson [A family of countable homogeneous graphs, Pacific J. Math. 38(1) (1971) 69–83] and denoted [Formula: see text], is the triangle-free analogue of the Rado graph. While the Ramsey theory of the Rado graph has been completely established, beginning with Erdős–Hajnal–Posá [Strong embeddings of graphs into coloured graphs, in Infinite and Finite Sets. Vol.[Formula: see text] , eds. A. Hajnal, R. Rado and V. Sós, Colloquia Mathematica Societatis János Bolyai, Vol. 10 (North-Holland, 1973), pp. 585–595] and culminating in work of S

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Hallas, James, and Ping Zhang. "On Strong Regal and Strong Royal Colorings." Journal of Combinatorial Mathematics and Combinatorial Computing 121, no. 1 (2024): 83–96. http://dx.doi.org/10.61091/jcmcc121-09.

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Two colorings have been introduced recently where an unrestricted coloring c assigns nonempty subsets of [ k ] = { 1 , … , k } to the edges of a (connected) graph G and gives rise to a vertex-distinguishing vertex coloring by means of set operations. If each vertex color is obtained from the union of the incident edge colors, then c is referred to as a strong royal coloring. If each vertex color is obtained from the intersection of the incident edge colors, then c is referred to as a strong regal coloring. The minimum values of k for which a graph G has such colorings are referred to as the st

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R, Gnanaprakasam, and Sahul Hamid I. "Gamma coloring of Mycielskian graphs." Indian Journal of Science and Technology 15, no. 20 (2022): 976–82. https://doi.org/10.17485/IJST/v15i20.2324.

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Abstract <strong>Background:</strong> Given a graph G, the gamma coloring problem seeks for a proper coloring C of G with the property that there exists a dominating set of G in which all the vertices receive different colors under the coloring C. The minimum number of colors required for a gamma coloring of G is called the gamma chromatic number of G and is denoted by cg (G). Our aim is to find the gamma chromatic number of Mycielskian graphs. <strong>Methods:</strong> Here, we obtain gamma coloring for Mycielskian graph m(G) from a gamma coloring of G by generalizing the give

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Dai, Zemiao, Muhammad Naeem, Zainab Shafaqat, Manzoor Ahmad Zahid, and Shahid Qaisar. "On the P3-Coloring of Bipartite Graphs." Mathematics 11, no. 16 (2023): 3487. http://dx.doi.org/10.3390/math11163487.

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The advancement in coloring schemes of graphs is expanding over time to solve emerging problems. Recently, a new form of coloring, namely P3-coloring, was introduced. A simple graph is called a P3-colorable graph if its vertices can be colored so that all the vertices in each P3 path of the graph have different colors; this is called the P3-coloring of the graph. The minimum number of colors required to form a P3-coloring of a graph is called the P3-chromatic number of the graph. The aim of this article is to determine the P3-chromatic number of different well-known classes of bipartite graphs

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Naduvath, Sudev. "Equitable coloring parameters of certain graph classes." Discrete Mathematics, Algorithms and Applications 10, no. 03 (2018): 1850040. http://dx.doi.org/10.1142/s1793830918500404.

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Coloring the vertices of a graph [Formula: see text] subject to given conditions can be considered as a random experiment and corresponding to this experiment, a discrete random variable [Formula: see text] can be defined as the color of a vertex chosen at random, with respect to the given type of coloring of [Formula: see text] and a probability mass function for this random variable can be defined accordingly. A proper coloring [Formula: see text] of a graph [Formula: see text], which assigns colors to the vertices of [Formula: see text] such that the numbers of vertices in any two color cla

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Khachatryan, H. H. "DEFICIENCY OF OUTERPLANAR GRAPHS." Proceedings of the YSU A: Physical and Mathematical Sciences 51, no. 1 (242) (2017): 22–28. http://dx.doi.org/10.46991/pysu:a/2017.51.1.022.

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An edge-coloring of a graph G with colors $1,2,...,t$ is an interval $t$-coloring, if all colors are used, and the colors of edges incident to each vertex of $G$ are distinct and form an interval of integers. A graph $G$ is interval colorable, if it has an interval $t$-coloring for some positive integer $t$. $def (G)$ denotes the minimum number of pendant edges that should be attached to $G$ to make it interval colorable. In this paper we study interval colorings of outerplanar graphs. In particular, we show that if $G$ is an outerplanar graph, then $def(G) \leq (|V(G)|-2)/(og(G)-2)$, where $o

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Yang, Hong, Muhammad Naeem, and Shahid Qaisar. "On the P3 Coloring of Graphs." Symmetry 15, no. 2 (2023): 521. http://dx.doi.org/10.3390/sym15020521.

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The vertex coloring of graphs is a well-known coloring of graphs. In this coloring, all of the vertices are assigned colors in such a way that no two adjacent vertices have the same color. We can call this type of coloring P2 coloring, where P2 is a path graph. However, there are situations in which this type of coloring cannot give us the solution to the problem at hand. To answer such questions, in this article, we introduce a novel graph coloring called P3 coloring. A graph is called P3-colorable if we can assign colors to the vertices of the graph such that the vertices of every P3 path ar

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Kristiana, Arika Indah, M. Hidayat, Robiatul Adawiyah, D. Dafik, Susi Setiawani, and Ridho Alfarisi. "ON LOCAL IRREGULARITY OF THE VERTEX COLORING OF THE CORONA PRODUCT OF A TREE GRAPH." Ural Mathematical Journal 8, no. 2 (2022): 94. http://dx.doi.org/10.15826/umj.2022.2.008.

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Let \(G=(V,E)\) be a graph with a vertex set \(V\) and an edge set \(E\). The graph \(G\) is said to be with a local irregular vertex coloring if there is a function \(f\) called a local irregularity vertex coloring with the properties: (i) \(l:(V(G)) \to \{ 1,2,...,k \} \) as a vertex irregular \(k\)-labeling and \(w:V(G)\to N,\) for every \(uv \in E(G),\) \({w(u)\neq w(v)}\) where \(w(u)=\sum_{v\in N(u)}l(i)\) and (ii) \(\mathrm{opt}(l)=\min\{ \max \{ l_{i}: l_{i} \ \text{is a vertex irregular labeling}\}\}\). The chromatic number of the local irregularity vertex coloring of \(G\) denoted by

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Labbate, Domenico, Davide Mattiolo, Giuseppe Mazzuoccolo, Federico Romaniello, and Gloria Tabarelli. "A Characterization of Graphs with Small Palette Index." Symmetry 15, no. 1 (2023): 154. http://dx.doi.org/10.3390/sym15010154.

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Given an edge-coloring of a graph G, we associate to every vertex v of G the set of colors appearing on the edges incident with v. The palette index of G is defined as the minimum number of such distinct sets, taken over all possible edge-colorings of G. A graph with a small palette index admits an edge-coloring which can be locally considered to be almost symmetric, since few different sets of colors appear around its vertices. Graphs with palette index 1 are r-regular graphs admitting an r-edge-coloring, while regular graphs with palette index 2 do not exist. Here, we characterize all graphs

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McCROAN, KEITH D., and R. C. LACHER. "REGION COLORING, EDGE COLORING, AND SCAN-CONVERSION OF MAPS." International Journal of Computational Geometry & Applications 04, no. 04 (1994): 423–55. http://dx.doi.org/10.1142/s0218195994000239.

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A theory is introduced relating extrinsic colorings of complementary regions of an embedded graph to certain intrinsic colorings of the edges of the graph, called color cycles, that satisfy a certain self-consistency condition. A region coloring is lifted to an edge coloring satisfying the cycle condition, and a dual construction builds a region coloring from any color cycle and any embedding of the graph. Both constructs are canonical, and the constructions are information-conservative in the sense that lifting an arbitrary region coloring to a color cycle and then reconstructing a region col

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A. Prasanna, M. A. Rifayathali, and S. Ismail Mohideen. "Hesitancy Fuzzy Graph Coloring." International Journal of Fuzzy Mathematical Archive 14, no. 02 (2017): 179–89. http://dx.doi.org/10.22457/ijfma.v14n2a2.

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Graph coloring dates back to 1852, when Francis Guthrie come up with the four color conjecture. Gary Chartrand and Ping Zhang [3] discussed various colorings of graph and its properties in their book entitled Chromatic Graph Theory. A graph coloring is the assignment of a color to each of the vertices or edges or both in such a way that no two adjacent vertices and incident edges share the same color. Graph coloring has been applied to many real world problems like scheduling, allocation, telecommunications and bioinformatics, etc.

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Caro, Yair, and Zsolt Tuza. "Monochromatic Graph Decompositions Inspired by Anti-Ramsey Theory and Parity Constraints." Mathematics 12, no. 23 (2024): 3665. http://dx.doi.org/10.3390/math12233665.

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We open here many new tracks of research in anti-Ramsey Theory, considering edge-coloring problems inspired by rainbow coloring and further by odd colorings and conflict-free colorings. Let G be a graph and F any given family of graphs. For every integer n≥|G|, let f(n,G|F) denote the smallest integer k such that any edge coloring of Kn with at least k colors forces a copy of G in which each color class induces a member of F. Observe that in anti-Ramsey problems, each color class is a single edge, i.e., F={K2}. Among the many results introduced in this paper, we mention the following. (1) For

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Sotskov, Yuri N. "Mixed Graph Colorings: A Historical Review." Mathematics 8, no. 3 (2020): 385. http://dx.doi.org/10.3390/math8030385.

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This paper presents a historical review and recent developments in mixed graph colorings in the light of scheduling problems with the makespan criterion. A mixed graph contains both a set of arcs and a set of edges. Two types of colorings of the vertices of the mixed graph and one coloring of the arcs and edges of the mixed graph have been considered in the literature. The unit-time scheduling problem with the makespan criterion may be interpreted as an optimal coloring of the vertices of a mixed graph, where the number of used colors is minimum. Complexity results for optimal colorings of the

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Jin, Xinze, and Shuangliang Tian. "Acyclic coloring of two operations of graphs." Journal of Physics: Conference Series 2964, no. 1 (2025): 012062. https://doi.org/10.1088/1742-6596/2964/1/012062.

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Abstract The coloring theory of graphs is a very important direction in graph theory. The graph coloring problem has a strong application background. Many practical problems such as timetabling problems, frequency allocation problems, traffic arrangements, circuit design, and storage problems can be transformed into graph coloring problems. A substantial amount of scholarly work has been dedicated to the exploration of acyclic coloring, resulting in a plethora of significant findings that significantly contribute to the theoretical framework of vertex coloring in graphs. An acyclic coloring of

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C. Paul Shyni. "Efficient Edge Chromatic Number Calculation Using Python:." Communications on Applied Nonlinear Analysis 32, no. 7s (2025): 718–24. https://doi.org/10.52783/cana.v32.3478.

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Graph coloring is one of the most important concept in graph theory and is used in many real time applications. Graph coloring includes, vertex coloring, edge coloring, region coloring etc., of graphs. Proper edge coloring means, coloring of edges of a graph such that no two adjacent edges have the same color. Edge chromatic number of a graph is the minimum number of colors required for proper edge coloring of the graph and is denoted by(G). In this article, GEC algorithm is proposed for finding the edge chromatic number of a graph with computer coding for the same using python. This proposed

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Zhong, Chuang, and Shuangliang Tian. "Neighbor Sum Distinguishing Edge (Total) Coloring of Generalized Corona Product." Journal of Physics: Conference Series 2381, no. 1 (2022): 012031. http://dx.doi.org/10.1088/1742-6596/2381/1/012031.

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Abstract The coloring theory of graphs is an important part of graph theory research. The key problem of the coloring theory of graphs is to determine the coloring number of each kind of coloring. Traditional coloring concepts mainly include proper vertex coloring, proper edge coloring, proper total coloring, and so on. In recent years, scholars at home and abroad have put forward some new coloring concepts, such as neighbor vertex distinguishing edge (total) coloring, and neighbor sum distinguishing edge (total) coloring, based on traditional coloring concepts and by adding other constraints.

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K.Kalaiarasi and L.Mahalakshmi. "Coloring of Regular and Strong Arcs Fuzzy Graphs." International Journal of Fuzzy Mathematical Archive 14, no. 01 (2017): 59–68. http://dx.doi.org/10.22457/ijfma.v14n1a8.

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In this paper, we introduce coloring of regular fuzzy graph G=(V,B). We can apply two different approaches to coloring of Regular fuzzy graph. The first approach is based on the odd regular coloring fuzzy graphs and the second approach is based on the even regular coloring fuzzy graph. We establish strong coloring of a fuzzy graph and we change δ − arc into α − arc or β − arc .

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Zhou, Yangyang, Dongyang Zhao, Mingyuan Ma, and Jin Xu. "Domination Coloring of Graphs." Mathematics 10, no. 6 (2022): 998. http://dx.doi.org/10.3390/math10060998.

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A domination coloring of a graph G is a proper vertex coloring of G, such that each vertex of G dominates at least one color class (possibly its own class), and each color class is dominated by at least one vertex. The minimum number of colors among all domination colorings is called the domination chromatic number, denoted by χdd(G). In this paper, we study the complexity of the k-domination coloring problem by proving its NP-completeness for arbitrary graphs. We give basic results and properties of χdd(G), including the bounds and characterization results, and further research χdd(G) of some

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Sreeja K S. "Fuzzy Dominator Coloring." Journal of Information Systems Engineering and Management 10, no. 44s (2025): 508–11. https://doi.org/10.52783/jisem.v10i44s.8880.

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Finding the right color for a graph while taking into account that each vertex in the graph dominates a whole color class is known as the dominator coloring problem. Fuzzy dominator coloring of certain regular graphs has been discussed here. Fuzzy dominator color and clique number of complete graphs, path graphs, and wheel graphs are related.

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Chartrand, Gary, James Hallas, and Ping Zhang. "Royal Colorings of Graphs." Ars Combinatoria 156 (July 31, 2023): 51–63. http://dx.doi.org/10.61091/ars156-06.

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For a graph \(G\) and a positive integer \(k\), a royal \(k\)-edge coloring of \(G\) is an assignment of nonempty subsets of the set \(\{1, 2, \ldots, k\}\) to the edges of \(G\) that gives rise to a proper vertex coloring in which the color assigned to each vertex \(v\) is the union of the sets of colors of the edges incident with \(v\). If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal \(k\)-coloring. The minimum positive integer \(k\) for which a graph has a strong royal \(k\)-coloring is the strong royal index of the graph. The primary emph

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Chartrand, Gary, James Hallas, and Ping Zhang. "Royal Colorings of Graphs." Ars Combinatoria 156 (July 31, 2023): 51–63. http://dx.doi.org/10.61091/ars156-6.

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For a graph G and a positive integer k , a royal k -edge coloring of G is an assignment of nonempty subsets of the set { 1 , 2 , … , k } to the edges of G that gives rise to a proper vertex coloring in which the color assigned to each vertex v is the union of the sets of colors of the edges incident with v . If the resulting vertex coloring is vertex-distinguishing, then the edge coloring is a strong royal k coloring. The minimum positive integer k for which a graph has a strong royal k -coloring is the strong royal index of the graph. The primary emphasis here is on strong royal colorings of

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Gurski, Frank, Dominique Komander, and Carolin Rehs. "Oriented Coloring on Recursively Defined Digraphs." Algorithms 12, no. 4 (2019): 87. http://dx.doi.org/10.3390/a12040087.

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Coloring is one of the most famous problems in graph theory. The coloring problem on undirected graphs has been well studied, whereas there are very few results for coloring problems on directed graphs. An oriented k-coloring of an oriented graph G = ( V , A ) is a partition of the vertex set V into k independent sets such that all the arcs linking two of these subsets have the same direction. The oriented chromatic number of an oriented graph G is the smallest k such that G allows an oriented k-coloring. Deciding whether an acyclic digraph allows an oriented 4-coloring is NP-hard. It follows

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Kowsalya, P., and D. Vijayalakshmi. "On Radio k – Chromatic Number for Mycielski of Some Graphs." Indian Journal Of Science And Technology 17, no. 39 (2024): 4129–37. http://dx.doi.org/10.17485/ijst/v17i39.2315.

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Objectives: In radio networks, the main difficulty is managing the radio spectrum, assigning radio frequencies to transmitters optimally without any interferences. This study aims to find the smallest span of Mycielski of some graphs, the maximum color assigned to any node is called span. Methods : This study focused on the problem of reducing interference by modeling it with a radio k - coloring problem on graphs. Where transmitters are modeled as nodes in a graph, with edges connecting nodes that represent transmitters in close proximity to one another. For a graph , with node set , edge set

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Naduvath, Sudev, and Johan Kok. "J-coloring of graph operations." Acta Universitatis Sapientiae, Informatica 11, no. 1 (2019): 95–108. http://dx.doi.org/10.2478/ausi-2019-0007.

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Abstract A vertex v of a given graph is said to be in a rainbow neighbourhood of G if every color class of G consists of at least one vertex from the closed neighbourhood N[v]. A maximal proper coloring of a graph G is a J-coloring if and only if every vertex of G belongs to a rainbow neighbourhood of G. In general all graphs need not have a J-coloring, even though they admit a chromatic coloring. In this paper, we characterise graphs which admit a J-coloring. We also discuss some preliminary results in respect of certain graph operations which admit a J-coloring under certain conditions.

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Septory, Brian Juned, Liliek Susilowati, Dafik Dafik, and M. Venkatachalam. "On Rainbow Antimagic Coloring of Joint Product of Graphs." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 4 (2023): 548–58. http://dx.doi.org/10.18860/ca.v7i4.17471.

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Let be a connected graph with vertex set and edge set . A bijection from to the set is a labeling of graph . The bijection is called rainbow antimagic vertex labeling if for any two edge and in path , where and . Rainbow antimagic coloring is a graph which has a rainbow antimagic labeling. Thus, every rainbow antimagic labeling induces a rainbow coloring G where the edge weight is the color of the edge . The rainbow antimagic connection number of graph is the smallest number of colors of all rainbow antimagic colorings of graph , denoted by . In this study, we studied rainbow antimagic colorin

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Muradyan, Levon N. "ON INTERVAL EDGE-COLORINGS OF COMPLETE MULTIPARTITE GRAPHS." Proceedings of the YSU A: Physical and Mathematical Sciences 56, no. 1 (257) (2022): 19–26. http://dx.doi.org/10.46991/pysu:a/2022.56.1.019.

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A graph $G$ is called a complete $r$-partite $(r\geq 2)$ graph, if its vertices can be divided into $r$ non-empty independent sets $V_1,\ldots,V_r$ in a way that each vertex in $V_i$ is adjacent to all the other vertices in $V_j$ for $1\leq i<j\leq r$. Let $K_{n_{1},n_{2},\ldots,n_{r}}$ denote a complete $r$-partite graph with independent sets $V_1,V_2,\ldots,V_r$ of sizes $n_{1},n_{2},\ldots,n_{r}$. An edge-coloring of a graph $G$ with colors $1,2,\ldots,t$ is called an \emph{interval $t$-coloring}, if all colors are used and the colors of edges incident to each vertex of $G$ are distinct

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Yusuf, Riduan, Fitria Puspa Dewi, Firmansyah Firmansyah, and Abdul Mujib. "Generalisasi Bilangan Kromatik Pada Beberapa Kelas Graf Korona." Jurnal Derivat: Jurnal Matematika dan Pendidikan Matematika 9, no. 2 (2022): 192–201. http://dx.doi.org/10.31316/jderivat.v9i2.3780.

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For example is a chromatic number with the smallest integer so that the graph has a true vertex coloring with k color. Chromatic number is still an interesting study which is still being studied for its development through graph coloring. Graph coloring is a special case of graph labeling. Labeling here means, giving color to the points at a certain limit so that no two vertices have the same color. This study aims to calculate the chromatic number in several classes of graphs including , , Based on the results of the study, generalization of the chromatic number of the graph class . Class and

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Durgun, Derya, and Busra Ozen-Dortok. "Packing chromatic number of transformation graphs." Thermal Science 23, Suppl. 6 (2019): 1991–95. http://dx.doi.org/10.2298/tsci190720363d.

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Graph coloring is an assignment of labels called colors to elements of a graph. The packing coloring was introduced by Goddard et al. [1] in 2008 which is a kind of coloring of a graph. This problem is NP-complete for general graphs. In this paper, we consider some transformation graphs and generalized their packing chromatic numbers.

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Vusuqi, Leila, Adel P. Kazemi, and Farshad Kazemnejad. "Total Dominator Total Chromatic Numbers of Some Graphs." Utilitas Mathematica 121, no. 1 (2024): 91–103. https://doi.org/10.61091/um121-07.

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Total dominator total coloring of a graph is a total coloring of the graph such that each object of the graph is adjacent or incident to every object of some color class. The minimum namber of the color classes of a total dominator total coloring of a graph is called the total dominator total chromatic number of the graph. Here, we will find the total dominator chromatic numbers of wheels, complete bipartite graphs and complete graphs.

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Wang, Yiqiao, Juan Liu, Yongtang Shi, and Weifan Wang. "Star Chromatic Index of 1-Planar Graphs." Symmetry 14, no. 6 (2022): 1177. http://dx.doi.org/10.3390/sym14061177.

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Many symmetric properties are well-explored in graph theory, especially in graph coloring, such as symmetric graphs defined by the automorphism groups, symmetric drawing of planar graphs, and symmetric functions which are used to count the number of specific colorings of a graph. This paper is devoted to studying the star edge coloring of 1-planar graphs. The star chromatic index χst′(G) of a graph G is defined as the smallest k for which the edges of G can be colored by using k colors so that no two adjacent edges get the same color and no bichromatic paths or cycles of length four are produc

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Shakila, M., and N. Rajakumari. "A Study on Radio Labeling of Diameter N-2 and Caterpillar Graphs." International Journal of Emerging Research in Management and Technology 6, no. 8 (2018): 30. http://dx.doi.org/10.23956/ijermt.v6i8.115.

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Radio labeling of graphs is a specific type of graph labeling. The basic type of graph labeling is vertex coloring; this is where the vertices of a graph G are assigned different colors so that adjacent vertices are not given the same color. A k-coloring of a graph G is a coloring that uses k colors. The chromatic number of a graph G is the minimum value for k such that a k-coloring exists for G [2].

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Sittitrai, Pongpat, Wannapol Pimpasalee, and Kittikorn Nakprasit. "(2, 4)-Colorability of Planar Graphs Excluding Cycles with 3, 4, and 6 Vertices." Mathematics 13, no. 11 (2025): 1762. https://doi.org/10.3390/math13111762.

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A defectivek-coloring is a coloring on the vertices of a graph with colors 1,2,…,k where adjacent vertices may have the same color. A (d1,d2)-coloring of a graph G is a defective two-coloring such that each vertex colored by i has at most di adjacent vertices of the same color, where i=1,2. A graph G is (d1,d2)-colorable if it admits (d1,d2)-coloring. For planar graphs excluding cycles with three, four, and six vertices, Dross and Ochem, and additionally Sittitrai and Pimpasalee, have studied their defective 2-coloring. They showed that such graphs are (0,6)- and (3,3)-colorable, respectively.

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Brannan, Michael, Priyanga Ganesan, and Samuel J. Harris. "The quantum-to-classical graph homomorphism game." Journal of Mathematical Physics 63, no. 11 (2022): 112204. http://dx.doi.org/10.1063/5.0072288.

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Motivated by non-local games and quantum coloring problems, we introduce a graph homomorphism game between quantum graphs and classical graphs. This game is naturally cast as a “quantum–classical game,” that is, a non-local game of two players involving quantum questions and classical answers. This game generalizes the graph homomorphism game between classical graphs. We show that winning strategies in the various quantum models for the game is an analog of the notion of non-commutative graph homomorphisms due to Stahlke [IEEE Trans. Inf. Theory 62(1), 554–577 (2016)]. Moreover, we present a g

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P, Kowsalya, and Vijayalakshmi D. "On Radio k – Chromatic Number for Mycielski of Some Graphs." Indian Journal of Science and Technology 17, no. 39 (2024): 4129–37. https://doi.org/10.17485/IJST/v17i39.2315.

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Abstract <strong>Objectives:</strong> In radio networks, the main difficulty is managing the radio spectrum, assigning radio frequencies to transmitters optimally without any interferences. This study aims to find the smallest span of Mycielski of some graphs, the maximum color assigned to any node is called span. <strong>Methods :</strong> This study focused on the problem of reducing interference by modeling it with a radio k - coloring problem on graphs. Where transmitters are modeled as nodes in a graph, with edges connecting nodes that represent transmitters in close proxim

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Mahmudah, Muhlisatul. "Aplikasi Pewarnaan Graf terhadap Penyimpanan Bahan Kimia." Jurnal Educazione : Jurnal Pendidikan, Pembelajaran dan Bimbingan dan konseling 10, no. 2 (2022): 108–15. http://dx.doi.org/10.56013/edu.v10i2.2024.

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Graf G = (V, E), where V is the set of points and E is the set of sides. An interesting application of graphs, one of which is graph coloring. There are three kinds of coloring that are point coloring, edge coloring, and region coloring. This paper will be studied dye staining. Point coloring is coloring the dots of a graph so that no two neighboring dots have the same color. The minimum number of colors that can be used to color a graph is expressed by chromatic numbers. Currently a lot of applications for graph coloring, one of which is the storage of chemicals. The storage of chemicals requ

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Fekete, Sándor P., and Phillip Keldenich. "Conflict-Free Coloring of Intersection Graphs." International Journal of Computational Geometry & Applications 28, no. 03 (2018): 289–307. http://dx.doi.org/10.1142/s0218195918500085.

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A conflict-free[Formula: see text]-coloring of a graph [Formula: see text] assigns one of [Formula: see text] different colors to some of the vertices such that, for every vertex [Formula: see text], there is a color that is assigned to exactly one vertex among [Formula: see text] and [Formula: see text]’s neighbors. Such colorings have applications in wireless networking, robotics, and geometry, and are well studied in graph theory. Here we study the conflict-free coloring of geometric intersection graphs. We demonstrate that the intersection graph of [Formula: see text] geometric objects wit

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. Adhira C, Ms. "Exploring Chromatic Polynomials: Theory and Applications in Graph Colouring." INTERNATIONAL JOURNAL OF SCIENTIFIC RESEARCH IN ENGINEERING AND MANAGEMENT 09, no. 06 (2025): 1–9. https://doi.org/10.55041/ijsrem49513.

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Abstract: Chromatic polynomials serve as a fundamental tool in graph theory for analyzing vertex colorings and counting the number of proper color assignments in graphs. This paper explores the theoretical foundation of chromatic polynomials, including key definitions, properties, and recursive computation methods such as the deletion-contraction technique. It also highlights practical applications in scheduling, register allocation, wireless frequency assignment, and social network analysis, demonstrating the broad relevance of graph coloring concepts in conflict-free resource allocation. Fin

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Goddard, Wayne, and Robert Melville. "Coloring subgraphs with restricted amounts of hues." Open Mathematics 15, no. 1 (2017): 1171–80. http://dx.doi.org/10.1515/math-2017-0098.

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Abstract We consider vertex colorings where the number of colors given to specified subgraphs is restricted. In particular, given some fixed graph F and some fixed set A of positive integers, we consider (not necessarily proper) colorings of the vertices of a graph G such that, for every copy of F in G, the number of colors it receives is in A. This generalizes proper colorings, defective coloring, and no-rainbow coloring, inter alia. In this paper we focus on the case that A is a singleton set. In particular, we investigate the colorings where the graph F is a star or is 1-regular.

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KIM, DONG HAN, and SEONHEE LIM. "Subword complexity and Sturmian colorings of regular trees." Ergodic Theory and Dynamical Systems 35, no. 2 (2013): 461–81. http://dx.doi.org/10.1017/etds.2013.50.

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AbstractIn this article, we discuss subword complexity of colorings of regular trees. We characterize colorings of bounded subword complexity and study Sturmian colorings, which are colorings of minimal unbounded subword complexity. We classify Sturmian colorings using their type sets. We show that any Sturmian coloring is a lifting of a coloring on a quotient graph of the tree which is a geodesic or a ray, with loops possibly attached, thus a lifting of an ‘infinite word’. We further give a complete characterization of the quotient graph for eventually periodic colorings.

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