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Journal articles on the topic '4-star graph'

Author: Grafiati

Published: 7 June 2025

Last updated: 2 August 2025

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1

E. Esakkiammal, Et al. "Triple Even Star Decomposition of Complete Bipartite Graphs." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 11 (2023): 479–83. http://dx.doi.org/10.17762/ijritcc.v11i11.9917.

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Let G be a finite, connected, undirected graph without loops or multiple edges. A decomposition {G2, G4, . . . , G2k} of G is said to be an even star decomposition if each Gi is a star and |E(Gi)| = i for all i = 2, 4, . . . , 2k. A graph G is said to have Triple Even Star Decomposition (TESD) if G can be decomposed into 3k stars {3S2, 3S4, . . . , 3S2k}. In this paper, we characterize Triple Even Star Decomposition of complete bipartite graphs Km,n when m = 2 and m = 3.

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2

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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3

Daming, Ahmad Syukur, and Yuliani Yuliani. "Dimensi Partisi Graf Hasil Amalgamasi Sisi Graf Roda dengan Graf Bintang." Euler : Jurnal Ilmiah Matematika, Sains dan Teknologi 12, no. 2 (2024): 139–44. https://doi.org/10.37905/euler.v12i2.27683.

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This study discusses the analysis of the partition dimension of the graph resulting from the edge amalgamation between the wheel graph ( Wn) and the star graph ( Sm), where the partition dimension is an important parameter in graph theory that serves to measure the minimum number of partitions required to distinguish every pair of vertices through a set of supporting vertices. The amalgamation process is carried out by merging one edge of the wheel graph with one edge of the star graph, thus forming a new graph. This research employs theoretical and algorithmic approaches to calculate the part

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4

Alivia, Alivia, Kartika Yulianti, and Yaya S. Kusumah. "The Chromatic Number of the Edge Corona Operation of Cycle Graph and Star Graph." Jurnal Matematika, Statistika dan Komputasi 21, no. 2 (2025): 431–38. https://doi.org/10.20956/j.v21i2.37361.

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One of the concepts in graph theory that can be analyzed is chromatic numbers of a graph and operation of two graphs. There are various kinds of operations of two graphs, one of which is the corona edge operation. This research aims to determine the chromatic number of the edge corona operation of graph Cn*K1,m and K1,m*Cn, where Cn is a cycle graph and K1,m is a star graph. The chromatic number is determined based on the pattern formed from several n and m values. The results of this research show that the chromatic number of the edge corona operation of graph Cn*K1,m is 4 for n= 3, 4, ... k

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5

Li, Mengya, and Wensong Lin. "On star family packing of graphs." RAIRO - Operations Research 55, no. 4 (2021): 2129–40. http://dx.doi.org/10.1051/ro/2021096.

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Let ℋ be a family of graphs. An ℋ-packing of a graph G is a set {G1, G2,…,Gk} of disjoint subgraphs of G such that each Gj is isomorphic to some element of ℋ. An ℋ-packing of a graph G that covers the maximum number of vertices of G is called a maximum ℋ-packing of G. The ℋ-packing problem seeks to find a maximum ℋ-packing of a graph. Let i be a positive integer. An i-star is a complete bipartite graph K1,i. This paper investigates the ℋ-packing problem with H being a family of stars. For an arbitrary family 𝒮 of stars, we design a linear-time algorithm for the 𝒮-packing problem in trees. Let

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6

Shindy Sagita Br Ginting and Mulyono Mulyono. "Bilangan Kromatik Dari Graf Hasil Operasi Korona Pada Graf Bintang Dan Graf Ligkaran." JURNAL RISET RUMPUN MATEMATIKA DAN ILMU PENGETAHUAN ALAM 2, no. 2 (2023): 263–69. http://dx.doi.org/10.55606/jurrimipa.v2i2.1622.

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Two graphs are operated with various operations, one of which is Operation Corona. The graphs that are operated in this paper are circle graphs and star graphs. Both graphs are operated with Operation Corona. The graph resulting from the operation is then colored using the Greedy Algorithm. The Chromatic Number obtained from the results of the Corona Operation on a graph (Cn ⊙ Sm) is χC_n⊙S_m = 3 for every m,n ≥ 3, {m,n ∈ N}. Because the graph resulting from the corona operation is non-commutative, the chromatic number obtained from the graph (Cn ⊙ Sm) is different from the graph (Sm ⊙ Cn). Th

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7

Dr., D. Angel Jovanna. "Relaxed Skolem Mean Labeling of 4 - Star Graph with Partition (3,1)." International Journal of Mathematics and Computer Research 13, no. 04 (2025): 5084–86. https://doi.org/10.5281/zenodo.15233852.

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To prove that the 4 - star graph  where  is a relaxed skolem mean graph if  ꞵ - α<sub>1 – </sub>α<sub>2 – </sub>α<sub>3 = </sub>6 is the core objective of this article.

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8

Chudamani. R, Mudda Ramesh, Raghupatruni Sunil Kumar, V. B. V. N. Prasad,. "Product of Semi – Lattices of Certain Graphs." Communications on Applied Nonlinear Analysis 31, no. 1 (2024): 231–37. http://dx.doi.org/10.52783/cana.v31.408.

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Introduction: In this article, author tries to construct a relation between graphs of product of meet-semilattices L = L_1 X L_2, where L_1 and L_2 are two semilattices and obtain some properties of such graphs. Author investigated that for meet-semilattices L_1 and L_2 has a cycle of length n-1 and n. Objectives: author reveals that if L_1 and L_2 be two meet-semilattices with 0 and L = L_1 X L_2, then it is a star graph. In this paper, we have covered some definitions, examples and theorems on zero devisor graph edge of a 4 - cycles or a 5 - cycles. Γ(L) is a star graph. Methods:

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9

LIN, CHENG-KUAN, JIMMY J. M. TAN, LIH-HSING HSU, EDDIE CHENG, and LÁSZLÓ LIPTÁK. "CONDITIONAL DIAGNOSABILITY OF CAYLEY GRAPHS GENERATED BY TRANSPOSITION TREES UNDER THE COMPARISON DIAGNOSIS MODEL." Journal of Interconnection Networks 09, no. 01n02 (2008): 83–97. http://dx.doi.org/10.1142/s0219265908002175.

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The diagnosis of faulty processors plays an important role in multiprocessor systems for reliable computing, and the diagnosability of many well-known networks has been explored. Zheng et al. showed that the diagnosability of the n-dimensional star graph Sn is n - 1. Lai et al. introduced a restricted diagnosability of multiprocessor systems called conditional diagnosability. They consider the situation when no faulty set can contain all the neighbors of any vertex in the system. In this paper, we study the conditional diagnosability of Cayley graphs generated by transposition trees (which inc

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10

Lau, G. C., and Y. H. Peng. "Chromaticity of complete 4-partite graphs with certain star or matching deleted." Applicable Analysis and Discrete Mathematics 4, no. 2 (2010): 253–68. http://dx.doi.org/10.2298/aadm100512023l.

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Let P(G,?) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ~ H, if P(G,?) = P(H,?). We write [G] = {H |H ~ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 4-partite graphs G accordingly to the number of 5-independent partitions of G. Using these results, we investigate the chromaticity of G with certain star or matching deleted. As a by-product, we obtain new families of chromatically unique complete 4-partite graphs with certain star or matching deleted.

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11

Deen, Mohamed R. Zeen El, and Nora A. Omar. "Similar d– even vertex odd mean labeling of diverse graphs." Journal of Information and Optimization Sciences 44, no. 7 (2023): 1365–96. http://dx.doi.org/10.47974/jios-1352.

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An injective function F where, F : V(G) → {0,2,4, ..., 2b + 2d - 2} is said to be d-even vertex odd mean labeling (d-EVOML) of the graph G(a, b) when the induced mapping F* : E(G) → {1,3, ..., 2b - 1} given by: F*(lw) = F(l)+F(w)/2, is a bijective function. A d - even vertex odd mean graph is a graph which allows even vertex odd mean labelling. In this study, we identify the lowest value of d for which the graphs: Y-tree, star graph, Px ʘ Kh, crown graph Rh, and rooted product Ph◊C4 have a d- even vertex odd mean labeling. Furthermore, we find the minimum number d for which the graphs: cycle g

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12

Thankachan, Reji, and Saritha Chandran. "Common multiples of paths and stars with complete graphs." Gulf Journal of Mathematics 12, no. 1 (2022): 1–14. http://dx.doi.org/10.56947/gjom.v12i1.780.

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A graph G is a common multiple of two graphs H1 and H2 if there exists a decomposition of G into edge-disjoint copies of H1 and also a decomposition of G into edge-disjoint copies of H2. If G is a common multiple of H1 and H2 and G has q edges, then we call G a (q, H1, H2) graph. Our paper deals with the following question: ''Given two graphs H1 and H2, for which values of q does there exist a (q, H1, H2) graph?'' when H1 is either a path or a star with 3 or 4 edges and H2 is a complete graph.

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13

Kim, Chaeeun, Changhun Han, and Ha-Myung Park. "UniCon: A unified star-operation to efficiently find connected components on a cluster of commodity hardware." PLOS ONE 17, no. 11 (2022): e0277527. http://dx.doi.org/10.1371/journal.pone.0277527.

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With a cluster of commodity hardware, how can we efficiently find all connected components of an enormous graph containing hundreds of billions of nodes and edges? The problem of finding connected components has been used in various applications such as pattern recognition, reachability indexing, graph compression, graph partitioning, and random walk. Several studies have been proposed to efficiently find connected components in various environments. Most existing single-machine and distributed-memory algorithms are limited in scalability as they have to load all data generated during the proc

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14

Chandran C., Saritha, and Reji T. "Common Multiples of Paths and Stars with Crowns." Proyecciones (Antofagasta) 43, no. 2 (2024): 331–44. http://dx.doi.org/10.22199/issn.0717-6279-5720.

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A graph $G$ is a common multiple of two graphs $H_1$ and $H_2$ if there exists a decomposition of $G$ into edge-disjoint copies of $H_1$ and also a decomposition of $G$ into edge-disjoint copies of $H_2$. If $ G $ is a common multiple of $H_1$ and $H_2$, and $ G $ has $ q $ edges, then we call $ G $ a $ (q, H_1, H_2) $ graph. Our paper deals with the following question: Given two graphs $ H_1 $ and $ H_2$, for which values of $ q $ does there exist a $ (q, H_1, H_2) $ graph? when $H_1$ is either a path or a star with $3$ or $4$ edges and $H_2$ is a crown.

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15

Lv, Ya Li, and Yong Hong Xiang. "The Conditional Connectivity of (n,k)-Star Graph." Advanced Materials Research 433-440 (January 2012): 4853–56. http://dx.doi.org/10.4028/www.scientific.net/amr.433-440.4853.

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Conditional connectivity has been proposed as an important parameter to estimate the fault tolerance of interconnection networks. In this paper, we consider the conditional connectivity of (n, k)-star graph. An (n, k)-star graph with dimension n (n ≥ 4) and order k can be partitioned into n subgraphs,. By utilizing this property, we give and proof the minimal cut-set and the minimal conditional cut-set of S n,k. We hence obtain that the conditional connectivity of (n, k)-star graph S n,k is n+k−3.

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16

Wang, Junzhen, Jinyu Zou, and Shumin Zhang. "Generalized 4-connectivity of hierarchical star networks." Open Mathematics 20, no. 1 (2022): 1261–75. http://dx.doi.org/10.1515/math-2022-0490.

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Abstract The connectivity is an important measurement for the fault-tolerance of a network. The generalized connectivity is a natural generalization of the classical connectivity. An S S -tree of a connected graph G G is a tree T = ( V ′ , E ′ ) T=\left(V^{\prime} ,E^{\prime} ) that contains all the vertices in S S subject to S ⊆ V ( G ) S\subseteq V\left(G) . Two S S -trees T T and T ′ T^{\prime} are internally disjoint if and only if E ( T ) ∩ E ( T ′ ) = ∅ E\left(T)\cap E\left(T^{\prime} )=\varnothing and V ( T ) ∩ V ( T ′ ) = S V\left(T)\cap V\left(T^{\prime} )=S . Denote by κ ( S ) \kappa

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17

Yousaf, Shamaila, Akhlaq Ahmad Bhatti, and Akbar Ali. "On the Minimum Variable Connectivity Index of Unicyclic Graphs with a Given Order." Discrete Dynamics in Nature and Society 2020 (July 18, 2020): 1–9. http://dx.doi.org/10.1155/2020/1217567.

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The variable connectivity index, introduced by the chemist Milan Randić in the first quarter of 1990s, for a graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a non-negative real number and dw is the degree of a vertex w in G. We call this index as the variable Randić index and denote it by Rvγ. In this paper, we show that the graph created from the star graph of order n by adding an edge has the minimum Rvγ value among all unicyclic graphs of a fixed order n, for every n≥4 and γ≥0.

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18

LIU, QINGHAI, ZHAO ZHANG, and ZHIHUA YU. "CYCLIC CONNECTIVITY OF STAR GRAPH." Discrete Mathematics, Algorithms and Applications 03, no. 04 (2011): 433–42. http://dx.doi.org/10.1142/s1793830911001322.

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For a connected graph G, a vertex subset F ⊂ V(G) is a cyclic vertex-cut of G if G - F is disconnected and at least two of its components contain cycles. The cardinality of a minimum cyclic vertex-cut of G, denoted by κc(G), is the cyclic vertex-connectivity of G. In this paper, we show that for any integer n ≥ 4, the n-dimensional star graph SGn has κc(SGn) = 6(n - 3).

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19

Azaizeh, Almothana, Roslan Hasni, Firas Haddad, Mutasem Alsmadi, Raed Alkhasawneh, and Asma Hamad. "4-total edge product cordial for some star related graphs." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 4 (2022): 4007. http://dx.doi.org/10.11591/ijece.v12i4.pp4007-4020.

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<p>Let G = (V (G), E(G)) be a graph, define an edge labeling function ψ from E(G) to {0, 1, . . . , k − 1} where k is an integer, 2 ≤ k ≤ |E(G)|, induces a vertex labeling function ψ∗ from V (G) to {0, 1, . . . , k − 1} such that ψ∗(v) = ψ(e1) × ψ(e2) × . . . × ψ(en) mod k where e1, e2, . . . , en are all edge incident to v. This function ψ is called a k-total edge product cordial (or simply k-TEPC) labeling of G if the absolute difference between number of vertices and edges labeling with i and number of vertices and edges labeling with j no more than 1 for all i, j ∈ {0, 1, . . . , k −

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20

Rajkumar, R., and P. Devi. "On permutability graphs of subgroups of groups." Discrete Mathematics, Algorithms and Applications 07, no. 02 (2015): 1550012. http://dx.doi.org/10.1142/s1793830915500123.

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The permutability graph of subgroups of a given group G, denoted by Γ(G), is a graph with vertex set consists of all the proper subgroups of G and two distinct vertices in Γ(G) are adjacent if and only if the corresponding subgroups permute in G. In this paper, we classify the finite groups whose permutability graphs of subgroups are one of bipartite, star graph, C3-free, C5-free, K4-free, K5-free, K1,4-free, K2,3-free or Pn-free (n = 2, 3, 4). We investigate the same for infinite groups also. Moreover, some results on the girth, completeness and regularity of the permutability graphs of subgr

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21

D., SRIRAM. "Union of 4-Total Mean Cordial Graph with the Star K1, N." International Journal of Innovative Science and Research Technology (IJISRT) 7, no. 2 (2024): 4. https://doi.org/10.5281/zenodo.10784511.

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Consider (p, q) graph G and define f from the vertex set V (G) to the set Zk where k ∈ N and k > 1. Foreache uv, assign the label f (u)+f (v) 2, Then the function f is called as k-total mean cordial labeling of G if number of vertices and edges labelled by i and not labelled by i differ by at most 1, wherei ∈ {0, 1, 2, · · · , k − 1}. Suppose a graph admits  a k-total mean cordial labeling then it is called as k- total mean cordial graph.In this paper we investigate  the 4-total mean cordial labeling of G ∪ K1,n where G is a 4-total mean co

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22

Almothana, AzaizehEn]U, Hasni Roslan, Haddad Firas, Alsmadi Mutasem, Alkhasawneh Raed, and Hamad Asma. "4-total edge product cordial for some star related graphs." International Journal of Electrical and Computer Engineering (IJECE) 12, no. 4 (2022): 4007–20. https://doi.org/10.11591/ijece.v12i4.pp4007-4020.

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Let G = (V (G),E(G)) be a graph, define an edge labeling function ψ from E(G) to {0, 1, . . . , k − 1} where k is an integer, 2 ≤ k ≤ |E(G)|, induces a vertex labeling function ψ&lowast; from V (G) to {0, 1, . . . , k − 1} such that ψ&lowast;(v) = ψ(e1) × ψ(e2) × . . . × ψ(en) mod k where e1, e2, . . . , en are all edge incident to v. This function ψ is called a k-total edge product cordial (or simply k-TEPC) labeling of G if the absolute difference between number of vertices and edges labeling with i and

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23

Lee, Hung-Chih. "Decomposing Kn,n into Hamiltonian cycles and small stars." International Journal of Contemporary Mathematical Sciences 20, no. 1 (2025): 89–97. https://doi.org/10.12988/ijcms.2025.92004.

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A decomposition of a graph $G$ is a set consisting of edge-disjoint subgraphs of $G$ whose union is $G$. A Hamiltonian cycle in $G$, is a cycle containing all of the vertices of $G$. A $m$-star is a star containing $m$ edges and denoted by $S_m$, which is isomorphic to the complete bipartite graph $K_{1,m}$. In this paper, the necessary and sufficient conditions for decomposing the balanced complete bipartite graph $K_{n,n}$ into $p$ copies of Hamiltonian cycles and $q$ copies of $3$-stars ($4$-stars) are given.

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24

DST, Ramesh, and Sopna SO. "Skolem Mean Labeling of Four Star Graphs K_(1,a_1 )∪ K_(1,a_2 )∪ K_(1,a_3 )∪ K_(1,b) where |b - (a_1+a_2+a_3)| = 4." Journal of Computational Mathematica 2, no. 1 (2018): 75–79. http://dx.doi.org/10.26524/jcm29.

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25

I, Gnanaselvi, and Ramesh D S T. "Non skolem mean labeling of a six star graph." Journal of Computational Mathematica 6, no. 1 (2022): 260–95. http://dx.doi.org/10.26524/cm134.

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A graph G = (V, E) with p vertices and q edges is said to be a Skolem mean graph if there exists a function f from the vertex set of G to {1, 2, 3, …, p} such that the induced map f * from the edge set of G to {2, 3, 4, …, p} defined by f∗(e = uv)= then the resulting edges get distinct labels from the set {2, 3, 4, …, p}.In this paper we prove that the six star graph G = 5K1,2

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26

Das, Kinkar Chandra. "On the Exponential Atom-Bond Connectivity Index of Graphs." Mathematics 13, no. 2 (2025): 269. https://doi.org/10.3390/math13020269.

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Several topological indices are possibly the most widely applied graph-based molecular structure descriptors in chemistry and pharmacology. The capacity of topological indices to discriminate is a crucial component of their study. In light of this, the literature has introduced the exponential vertex-degree-based topological index. The exponential atom-bond connectivity index is defined as follows: eABC=eABC(Υ)=∑vivj∈E(Υ)edi+dj−2didj, where di is the degree of the vertex vi in Υ. In this paper, we prove that the double star DSn−3,1 is the second maximal graph with respect to the eABC index of

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27

Agustin, Ika Hesti, Dafik Dafik, N. Mohanapriya, Marsidi Marsidi, and Ismail Naci Cangul. "The Distance Irregular Reflexive k-Labeling of Graphs." CAUCHY: Jurnal Matematika Murni dan Aplikasi 7, no. 4 (2023): 622–30. http://dx.doi.org/10.18860/ca.v7i4.19747.

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A total k-labeling is a function fe from the edge set to the set {1, 2, . . . , ke} and a function fv from the vertex set to the set {0, 2, 4, . . . , 2kv}, where k = max{ke, 2kv}. A distance irregular reflexive k-labeling of the graph G is the total k-labeling, if for every two different vertices u and u 0 of G, w(u) 6= w(u 0 ), where w(u) = Σui∈N(u)fv(ui) + Σuv∈E(G)fe(uv). The minimum k for graph G which has a distance irregular reflexive k-labelling is called distance reflexive strength of the graph G, denoted by Dref (G). In this paper, we determine the exact value of distance reflexive st

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Xu, Xin, Xu Zhang, and Jiawei Shao. "Planar Turán number of double star $ S_{3, 4} $." AIMS Mathematics 10, no. 1 (2025): 1628–44. https://doi.org/10.3934/math.2025075.

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<p>Planar Turán number, denoted by $ \mathrm{ex}_{\mathcal{P}}(n, H) $, is the maximum number of edges in an $ n $-vertex planar graph which does not contain $ H $ as a subgraph. Ghosh, Győri, Paulos and Xiao initiated the topic of the planar Turán number for double stars. There were two double stars $ S_{3, 4} $ and $ S_{3, 5} $ that remained unknown. In this paper, we give the exact value of $ \mathrm{ex}_{\mathcal{P}}(n, S_{3, 4}) $.</p>

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Wang, Li. "Uniformly resolvable decompositions of λ-fold complete multipartite graph into 4-star". Filomat 39, № 5 (2025): 1717–33. https://doi.org/10.2298/fil2505717w.

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Let ?Ku [1] be the ?-fold complete multipartite graph with u parts of size 1. A (K1,n, ?)-resolvable group divisible design (RGDD) of type gu is a K1,n-decomposition of the graph ?Ku [g] into parallel classes each of which is a partition of the vertex set. A (K1,n, ?)-frame of type gu is a K1,n-decomposition of ?Ku [g] into partial parallel classes each of which is a partition of the vertex set except for those vertices in one of the u parts. In this paper, we completely solve the existence of a (K1,4, ?)-frame and a (K1,4, ?)-RGDD of type gu for any admissible parameters g, u and ?.

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30

Shen, Xiaojun, Qing Hu, Bin Cong, Hal Sudborough, Mike Girou, and Said Bettayeb. "The 4-star graph is not a subgraph of any hypercube." Information Processing Letters 45, no. 4 (1993): 199–203. http://dx.doi.org/10.1016/0020-0190(93)90119-t.

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31

Lortz, Roland, and Ingrid Mengersen. "On the Ramsey numbers \(r(S_n, K_6-3K_2)\)." Journal of Combinatorial Mathematics and Combinatorial Computing 124 (March 17, 2025): 229–34. https://doi.org/10.61091/jcmcc124-15.

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For every connected graph \(F\) with \(n\) vertices and every graph \(G\) with chromatic surplus \(s(G)\leq n\), the Ramsey number \(r(F,G)\) satisfies \( r(F,G) \geq (n-1)(\chi(G)-1) + s(G), \) where \(\chi(G)\) denotes the chromatic number of \(G\). If this lower bound is attained, then \(F\) is called \(G\)-good. For all connected graphs \(G\) with at most six vertices and \(\chi(G) \geq 4\), every tree \(T_n\) of order \(n\geq 5\) is \(G\)-good. In case of \(\chi(G) = 3\) and \(G \neq K_6-3K_2\), every non-star tree \(T_n\) is \(G\)-good except for some small \(n\), whereas \(r(S_n,G)\) fo

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32

NAGY, DÁNIEL T. "On the Number of 4-Edge Paths in Graphs With Given Edge Density." Combinatorics, Probability and Computing 26, no. 3 (2016): 431–47. http://dx.doi.org/10.1017/s0963548316000389.

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We investigate the number of 4-edge paths in graphs with a given number of vertices and edges, proving an asymptotically sharp upper bound on this number. The extremal construction is the quasi-star or the quasi-clique graph, depending on the edge density. An easy lower bound is also proved. This answer resembles the classic theorem of Ahlswede and Katona about the maximal number of 2-edge paths, and a recent theorem of Kenyon, Radin, Ren and Sadun about k-edge stars.

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Putri, Azizah Riana, Syafrizal Sy, and Monika Rianti Helmi. "Bilangan Kromatik Lokasi Graf Tentakel." Limits: Journal of Mathematics and Its Applications 22, no. 2 (2025): 45–53. https://doi.org/10.12962/limits.v22i2.3462.

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The locating-chromatic number of a graph was introduced by Chartrand et al. in 2002, which is a combined concept between the vertex coloring and partition dimension of a graph. The locating-chromatic number of a graph is a grouping of vertices on a graph based on color, which is called a color class, provided that each vertex on the graph has a different color code. Determining the locating-chromatic number of a graph is done by constructing the lower and upper bound of the locating-chromatic number of the graph. In this paper, we determine the locating-chromatic number of the tentacle graph,

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Monikandan, S., and S. Sundar Raj. "Adversary degree associated reconstruction number of graphs." Discrete Mathematics, Algorithms and Applications 07, no. 01 (2015): 1450069. http://dx.doi.org/10.1142/s1793830914500694.

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A vertex-deleted subgraph of a graph G is called a card of G. A card of G with which the degree of the deleted vertex is also given is called a degree associated card or dacard of G. The adversary degree associated reconstruction number of a graph G, adrn (G), is the minimum number k such that every collection of k dacards of G uniquely determines G. We prove that adrn (G) = 1 + min {t+1, m-t} or 1 + min {t, m - t + 2} for a graph G obtained by subdividing t edges of K1, m. We also prove that if G is a nonempty disconnected graph whose components are cycles or complete graphs, then adrn (G) is

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HU, XIAOLAN, YUNQING ZHANG, and YANBO ZHANG. "QUADRILATERAL-TREE PLANAR RAMSEY NUMBERS." Bulletin of the Australian Mathematical Society 97, no. 2 (2018): 194–99. http://dx.doi.org/10.1017/s0004972717001022.

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For two given graphs $G_{1}$ and $G_{2}$, the planar Ramsey number $PR(G_{1},G_{2})$ is the smallest integer $N$ such that every planar graph $G$ on $N$ vertices either contains $G_{1}$, or its complement contains $G_{2}$. Let $C_{4}$ be a quadrilateral, $T_{n}$ a tree of order $n\geq 3$ with maximum degree $k$, and $K_{1,k}$ a star of order $k+1$. We show that $PR(C_{4},T_{n})=\max \{n+1,PR(C_{4},K_{1,k})\}$. Combining this with a result of Chen et al. [‘All quadrilateral-wheel planar Ramsey numbers’, Graphs Combin.33 (2017), 335–346] yields exact values of all the quadrilateral-tree planar R

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HERMILLER, SUSAN, DEREK F. HOLT, and SARAH REES. "STAR-FREE GEODESIC LANGUAGES FOR GROUPS." International Journal of Algebra and Computation 17, no. 02 (2007): 329–45. http://dx.doi.org/10.1142/s0218196707003603.

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In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions C′(1/6) and C′(1/4) - T(4) has the property that the set of all geodesics (over the same generating set) is a star-free regular language. Star-free regularity of the geodesic set is shown to be dependent on the generating set chosen, even for free groups. We also show that the class of groups whose geodesic sets are star-free with respect to some generating set is closed under taking graph (and hence free and direct) products, and includes all virtually abelian groups

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Milosevic, Marko. "An example of using star complements in classifying strongly regular graphs." Filomat 22, no. 2 (2008): 53–57. http://dx.doi.org/10.2298/fil0802053m.

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Ramane, H. S., D. S. Revankar, Ivan Gutman, and H. B. Walikar. "Distance spectra and distance energies of iterated line graphs of regular graphs." Publications de l'Institut Math?matique (Belgrade) 85, no. 99 (2009): 39–46. http://dx.doi.org/10.2298/pim0999039r.

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The distance or D-eigenvalues of a graph G are the eigenvalues of its distance matrix. The distance or D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. Two graphs G1 and G2 are said to be D-equienergetic if ED(G1) = ED(G2). Let F1 be the 5-vertex path, F2 the graph obtained by identifying one vertex of a triangle with one end vertex of the 3-vertex path, F3 the graph obtained by identifying a vertex of a triangle with a vertex of another triangle and F4 be the graph obtained by identifying one end vertex of a 4-vertex star with a middle vertex of a 3-vertex

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39

Rücker, Gerta, Christoph Rücker, and Ivan Gutman. "On Kites, Comets, and Stars. Sums of Eigenvector Coefficients in (Molecular) Graphs." Zeitschrift für Naturforschung A 57, no. 3-4 (2002): 143–53. http://dx.doi.org/10.1515/zna-2002-3-406.

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Two graph invariants were encountered that form the link between (molecular) walk counts and eigenvalues of graph adjacency matrices. In particular, the absolute value of the sum of coefficients of the first or principal (normalized) eigenvector, s1, and the analogous quantity sn, pertaining to the last eigenvector, appear in equations describing some limits (for infinitely long walks) of relative frequencies of several walk counts. Quantity s1 is interpreted as a measure of mixedness of a graph, and sn, which plays a role for bipartite graphs only, is interpreted as a measure of the imbalance

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Deng, Fei, Huiqin Jiang, Jia-Bao Liu, et al. "The Sanskruti index of trees and unicyclic graphs." Open Chemistry 17, no. 1 (2019): 448–55. http://dx.doi.org/10.1515/chem-2019-0046.

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AbstractThe Sanskruti index of a graph G is defined as $$\begin{align*}S(G)=\sum_{uv\in{}E(G)}{\left(\frac{s_G(u)s_G(v)}{s_G(u)+s_G(v)-2}\right)}^3, \end{align*}$$where sG(u) is the sum of the degrees of the neighbors of a vertex u in G. Let Pn, Cn, Sn and Sn + e be the path, cycle, star and star plus an edge of n vertices, respectively. The Sanskruti index of a molecular graph of a compounds can model the bioactivity of compounds, has a strong correlation with entropy of octane isomers and its prediction power is higher than many existing topological descriptors.In this paper, we investigate

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Hu, Shuo-Cheng, and Chang-Biau Yang. "Fault Tolerance on Star Graphs." International Journal of Foundations of Computer Science 08, no. 02 (1997): 127–42. http://dx.doi.org/10.1142/s0129054197000112.

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The capability of fault tolerance is one of the advantages of multiprocessor systems. In this paper, we prove that the fault tolerance of an n-star graph is 2n-5 with restriction to the forbidden faulty set. And we propose an algorithm for examining the connectivity of an n-star graph when there exist at most 2n - 4 faults. The algorithm requires O(n2 log n) time. Besides, we improve the fault-tolerant routing algorithm proposed by Bagherzadeh et al. by calculating the cycle structure of a permutation and the avoidance of routing message to a node without any nonfaulty neighbor. This calculati

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Ilayaraja, M., and A. Muthusamy. "Decomposition of Complete Graphs into Paths and Stars with Different Number of Edges." Journal of Combinatorial Mathematics and Combinatorial Computing 122, no. 1 (2024): 301–16. http://dx.doi.org/10.61091/jcmcc122-25.

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Let P n and K n respectively denote a path and complete graph on n vertices. By a { p H 1 , q H 2 } -decomposition of a graph G , we mean a decomposition of G into p copies of H 1 and q copies of H 2 for any admissible pair of nonnegative integers p and q , where H 1 and H 2 are subgraphs of G . In this paper, we show that for any admissible pair of nonnegative integers p and q , and positive integer n ≥ 4 , there exists a { p P 4 , q S 4 } -decomposition of K n if and only if 3 p + 4 q = ( n 2 ) , where S 4 is a star with 4 edges.

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Wardani, Ayu Anisa, Lucia Ratnasari, Robertus Heri Soelistyo Utomo, and Siti Khabibah. "Inverse Domination Number and Inverse Total Domination of Sierpinski Star Graph." International Journal of Mathematics and Statistics Studies 12, no. 3 (2024): 71–79. http://dx.doi.org/10.37745/ijmss.13/vol12n37179.

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Given a graph G=(V(G),E(G)) consisting of the set of vertices V(G) and the set of edges E(G). For example, D(G) is a domination set of graph G with minimum cardinality, if V(G)-D(G) contains a domination set D^(-1) (G), then D^(-1) (G) is called the inverse domination set of graph G. The minimum cardinality of the inverse domination set of the graph G is called the inverse domination number, denoted by γ^(-1) (G). If D_t (G) is the total domination set of the graph G with minimal cardinality, and V(G)-D_t (G) contains the total domination set D_t^(-1) (G), then D_t^(-1) (G) is called the inver

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Petrenjuk, Volodymyr, Dmytro Petreniuk, and Oleh Oryshaka. "Structure of Projective Planar Subgraphs of the Graph Obstructions for Fixed Surface." Cybernetics and Computer Technologies, no. 2 (September 30, 2022): 13–30. http://dx.doi.org/10.34229/2707-451x.22.2.2.

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Consider the problem of studying the metric properties of a subgraph G\v, where v is an arbitrary vertex of obstruction graphs G of a nonorientable genus, which will determine the sets of points of attachment of one subgraph to another and allow constructing prototypes of graphs-obstruction with number of vertices greater than 10 nonorientable genus greater than 1. This problem is related to Erdosh's hypothesis [3] on the coverage of obstruction graphs of an undirected surface of the genus k, where k > 0, the smallest inclusion of the set of k + 1st graph of the homeomorphic K5, or K3,3, in

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Khorsandi, Mahdi Reza, and Atefeh Shekofteh. "On the line graphs of zero-divisor graphs of posets." Journal of Algebra and Its Applications 16, no. 07 (2016): 1750121. http://dx.doi.org/10.1142/s0219498817501213.

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In this paper, we study the zero-divisor graph [Formula: see text] of a poset [Formula: see text] and its line graph [Formula: see text]. We characterize all posets whose [Formula: see text] are star, finite complete bipartite or finite. Also, we prove that the diameter of [Formula: see text] is at most 3 while its girth is either 3, 4 or [Formula: see text]. We also characterize [Formula: see text] in terms of their diameter and girth. Finally, we classify all posets [Formula: see text] whose [Formula: see text] are planar.

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Jent, Emma, Sawyer Osborn, and Ping Zhang. "Extending Ramsey Numbers for Connected Graphs of Size 3." Symmetry 16, no. 8 (2024): 1092. http://dx.doi.org/10.3390/sym16081092.

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It is well known that the famous Ramsey number R(K3,K3)=6. That is, the minimum positive integer n for which every red-blue coloring of the edges of the complete graph Kn results in a monochromatic triangle K3 is 6. It is also known that every red-blue coloring of K6 results in at least two monochromatic triangles, which need not be vertex-disjoint or edge-disjoint. This fact led to an extension of Ramsey numbers. For a graph F and a positive integer t, the vertex-disjoint Ramsey number VRt(F) is the minimum positive integer n such that every red-blue coloring of the edges of the complete grap

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LI, TONGYANG. "AN IMPROVED COURNOT COMPETITION MODEL: CONSIDERATION OF MARKET SHARE OBJECTIVE." Discrete Mathematics, Algorithms and Applications 06, no. 01 (2014): 1450005. http://dx.doi.org/10.1142/s1793830914500050.

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Cournot competition model calculates profit by company's product quantity, but it does not take market share objective into consideration. It has obstacles of considering nonlinear aspects because the partial derivative equations are very hard to solve. Our algorithm both improves Cournot's model with consideration of market share ratio, and avoids the difficulty of solving several partial derivative equations directly. In our algorithm, we give a parameter σ to describe a company's consideration of market share objective, formulate the competition between companies, and calculate new market s

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48

Qiang, Xiaoli, Saeed Kosari, Zehui Shao, Seyed Mahmoud Sheikholeslami, Mustapha Chellali, and Hossein Karami. "A Note on the Paired-Domination Subdivision Number of Trees." Mathematics 9, no. 2 (2021): 181. http://dx.doi.org/10.3390/math9020181.

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For a graph G with no isolated vertex, let γpr(G) and sdγpr(G) denote the paired-domination and paired-domination subdivision numbers, respectively. In this note, we show that if T is a tree of order n≥4 different from a healthy spider (subdivided star), then sdγpr(T)≤min{γpr(T)2+1,n2}, improving the (n−1)-upper bound that was recently proven.

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Ódor, Gergely, and Patrick Thiran. "Sequential metric dimension for random graphs." Journal of Applied Probability 58, no. 4 (2021): 909–51. http://dx.doi.org/10.1017/jpr.2021.16.

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AbstractIn the localization game on a graph, the goal is to find a fixed but unknown target node $v^\star$ with the least number of distance queries possible. In the jth step of the game, the player queries a single node $v_j$ and receives, as an answer to their query, the distance between the nodes $v_j$ and $v^\star$ . The sequential metric dimension (SMD) is the minimal number of queries that the player needs to guess the target with absolute certainty, no matter where the target is.The term SMD originates from the related notion of metric dimension (MD), which can be defined the same way a

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Li, Yalan, Shumin Zhang, and Chengfu Ye. "On Cyclic-Vertex Connectivity of n , k -Star Graphs." Mathematical Problems in Engineering 2021 (April 12, 2021): 1–4. http://dx.doi.org/10.1155/2021/5570761.

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A vertex subset F ⊆ V G is a cyclic vertex-cut of a connected graph G if G − F is disconnected and at least two of its components contain cycles. The cyclic vertex-connectivity κ c G is denoted as the cardinality of a minimum cyclic vertex-cut. In this paper, we show that the cyclic vertex-connectivity of the n , k -star network S n , k is κ c S n , k = n + 2 k − 5 for any integer n ≥ 4 and k ≥ 2 .

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