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Journal articles on the topic 'Double Triangular Snake Graphs'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

Barasara, Chirag, and Palak Prajapati. "Antimagic Labeling for Some Snake Graphs." Proyecciones (Antofagasta) 43, no. 2 (2024): 521–37. http://dx.doi.org/10.22199/issn.0717-6279-6005.

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A graph with q edges is called antimagic if its edges can be labeled with 1, 2, 3, ..., q without repetition such that the sums of the labels of the edges incident to each vertex are distinct. In this paper we study antimagic labeling of double triangular snake, alternate triangular snake, double alternate triangular snake, quadrilateral snake, double quadrilateral snake, alternate quadrilateral snake, double alternate quadrilateral snake.

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2

Anitha, H., S. K. Sowjanya, Shanmukha B, and K. R. Karthik. "K - Power-3 Heronian Mean Labeling of Graphs." International Journal of Mathematics and Computer Research 12, no. 11 (2024): 4571–76. https://doi.org/10.5281/zenodo.14191351.

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We describe a function  as  – Power 3. If constitute both the induced edge labelling and take be an injective function and express it as, then a graph's Heronian Mean Labelling  with p nodes and q lines is  or  with distinct edge labels. In this manuscript we have proved the – Power -3 Mean labeling behaviour of Path, Twig Graph, Triangular ladder . We have also investigated  - Super power -3 Heronian Mean labelling of graghs. Also, we prove that  is not – Power - 3 Heronian Mean graph and  - Super power -3 Heronian Mean labelling of Sn

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3

Ponraj, R., M. Maria Adaickalam, and R. Kala. "3-Difference cordial labeling of some path related graphs." Indonesian Journal of Combinatorics 2, no. 1 (2018): 1. http://dx.doi.org/10.19184/ijc.2018.2.1.1.

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<p>Let G be a (p, q) graph. Let f : V (G) → {1, 2, . . . , k} be a map where k is an integer 2 ≤ k ≤ p. For each edge uv, assign the label |f(u) − f(v)|. f is called k-difference cordial labeling of G if |vf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x, ef (1) and ef (0) respectively denote the number of edges labelled with 1 and not labelled with 1. A graph with a k-difference cordial labeling is called a k-difference cordial graph. In this paper we investigate 3-difference cordial labeling behavior of triangular snake, alternat

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4

A. Anat Jaslin Jini. "Relatively Prime Domination Number in Triangular Snake Graphs." Advances in Nonlinear Variational Inequalities 28, no. 2 (2024): 159–65. http://dx.doi.org/10.52783/anvi.v28.1912.

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A set S⊆V is said to be relatively prime dominating set if it is a dominating set with at least two elements and for every pair of vertices u and v in S, (deg⁡(u),deg⁡〖(v))〗=1 and the minimum cardinality of a relatively prime dominating set is called relatively prime domination number and it is denoted by γ_rpd (G). If there is no such pair exist, then γ_rpd (G)=0. For a finite undirected graph G(V,E) and a subset V, the switching of G by is defined as the graph (V, ) which is obtained from G by removing all edges between and its complement V- and adding as edges all non-edges between and V- .

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5

Princy Kala, V. "k-super cube root cube mean labeling of graphs." Proyecciones (Antofagasta) 40, no. 5 (2021): 1097–116. http://dx.doi.org/10.22199/issn.0717-6279-4258.

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Consider a graph G with |V (G)| = p and |E(G)| = q and let f : V (G) → {k, k + 1, k + 2, . . . p + q + k − 1}} be an injective function. The induced edge labeling f ∗ for a vertex labeling f is defined by f ∗ (e) = for all e = uv ∈ E(G) is bijective. If f(V (G)) ∪ {f ∗ (e) : e ∈ E(G)} = {k, k + 1, k + 2, . . . , p + q + k − 1}, then f is called a k-super cube root cube mean labeling. If such labeling exists, then G is a k-super cube root cube mean graph. In this paper, I introduce k-super cube root cube mean labeling and prove the existence of this labeling to the graphs viz., triangular snake

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Utomo, Robertus Heri, Heru Tjahjana, Bambang Irawanto, and Lucia Ratnasari. "PELABELAN TOTAL SUPER TRIMAGIC SISI PADA BEBERAPA GRAF." Journal of Fundamental Mathematics and Applications (JFMA) 1, no. 1 (2018): 52. http://dx.doi.org/10.14710/jfma.v1i1.4.

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This paper is addressed to discuss the edge super trimagic total labeling on some graphs which are corona, double ladder, quadrilateral snake and alternate triangular snake. The main results are the edge super trimagic total label for these graphs. Furthermore, it was prove that corona is a graph with edge super trimagic total labeling, a double ladder with odd ladder is graph with edge super trimagic total labeling, quadrilateral snake is a graph with edge super trimagic total labeling and finally an alternate triangular snake with odd ladder is graph with edge super trimagic total labeling.

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7

K.Sunitha. "Radio Labeling of Double Triangular Snake Graphs." Annals of Pure and Applied Mathematics 37, no. 49 (2023): 63–71. http://dx.doi.org/10.22457/apam.v27n2a04905.

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8

Jeyanthi, P., A. Maheswari, and M. Vijayalakshmi. "3-product cordial labeling of some snake graphs." Proyecciones (Antofagasta) 38, no. 1 (2019): 13–30. https://doi.org/10.22199/issn.0717-6279-3409.

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Let G be a (p,q) graph. A mapping ? : V (G) → {0, 1, 2} is called 3-product cordial labeling if |v?(i) − v? (j)| ≤ 1 and |e? (i) − e? (j)| ≤ 1 for any i, j ∈ {0, 1, 2},where v? (i) denotes the number of vertices labeled with i, e? (i) denotes the number of edges xy with ?(x)?(y) ≡ i(mod3). A graph with 3-product cordial labeling is called 3-product cordial graph. In this paper we investigate the 3-product cordial behavior of alternate triangular snake, double alternate triangular snake and triangular snake graphs.

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9

ELrokh, Ashraf, Elsayed Badr, Mohammed M. Ali Al-Shamiri, and Shimaa Ramadhan. "Upper Bounds of Radio Number for Triangular Snake and Double Triangular Snake Graphs." Journal of Mathematics 2022 (May 16, 2022): 1–8. http://dx.doi.org/10.1155/2022/3635499.

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A radio labeling of a simple connected graph G = V , E is a function h : V ⟶ N such that h x − h y ≥ diam G + 1 − d x , y , where diam G is the diameter of graph and d(x, y) is the distance between the two vertices. The radio number of G , denoted by rn G , is the minimum span of a radio labeling for G . In this study, the upper bounds for radio number of the triangular snake and the double triangular snake graphs are introduced. The computational results indicate that the presented upper bounds are better than the results of the mathematical model provided by Badr and Moussa in 2020. On the c

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10

A., Josephine Lissie, and Jaya S. "TRIPLE CONNECTED DOMINATION NUMBER FOR SOME SPECIAL GRAPHS." International Journal of Current Research and Modern Education, Special Issue (August 11, 2017): 10–12. https://doi.org/10.5281/zenodo.841822.

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A subset <em>S</em> of <em>V</em> of a nontrivial connected graph <em>G</em> is said to be a triple connected dominating set (tcd-set), if <em>S</em> is a dominating set and the induced subgraph<em>S</em>is triple connected. The minimum cardinality taken over all triple connected dominating sets is called the triple connected domination number of <em>G</em> and is denoted by γ<em><sub>tc</sub></em>(<em>G</em>). Any triple connected dominating set with γ<em><sub>tc</sub></em> vertices is called a γ<em><sub>tc</sub></em>-set of <em>G</em>. In this paper we obtain triple connected domination numb

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11

Shahid, Malik Muhammad Suleman, Muhammad Ishaq, Anuwat Jirawattanapanit, and Khanyaluck Subkrajang. "Depth and Stanley depth of the edge ideals of multi triangular snake and multi triangular ouroboros snake graphs." AIMS Mathematics 7, no. 9 (2022): 16449–63. http://dx.doi.org/10.3934/math.2022900.

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<abstract><p>In this paper, we study depth and Stanley depth of the quotient rings of the edge ideals associated to triangular and multi triangular snake and triangular and multi triangular ouroboros snake graphs. In some cases, we find exact values, otherwise, we find tight bounds. We also find lower bounds for the edge ideals of triangular and multi triangular snake and ouroboros snake graphs and prove a conjecture of Herzog for all edge ideals we considered.</p></abstract>

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12

Shanthakumari, A., and S. Deepalakshmi. "Hosoya Index of Triangular and Alternate Triangular Snake Graphs." Procedia Computer Science 172 (2020): 240–46. http://dx.doi.org/10.1016/j.procs.2020.05.038.

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13

Muhammad Imran. "Computation of Lucky Number of Comb Graphs Cfw, Cgw, Chw and Triangular Snake, Alternate Triangular Snake Graphs." Power System Technology 48, no. 1 (2024): 1381–94. https://doi.org/10.52783/pst.399.

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Let λ:V(Ω)→{1, 2,..., z} be a mapping of vertices of a graph Ω. Let S(x) denote the sum of labels of the neighbors of the vertex x in Ω. If vertex x has degree zero, we put S(x)=0. A mapping λ is categorized as lucky labeling if S(x)=S(y) for every pair of adjacent vertices x and y. The lucky number of graph Ω, denoted by η (Ω), is the least positive integer z used to label vertices to form lucky labeling. In this paper, we demonstrate that different families of comb graph and snake graph are lucky labeled graphs. We also calculate the exact value of the lucky number for the aforementioned gra

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14

S. K. Vaidya and N B Vyas. "Product cordial labeling for alternate snake graphs." Malaya Journal of Matematik 2, no. 03 (2014): 188–96. http://dx.doi.org/10.26637/mjm203/002.

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15

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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16

hya, S. S. Sand, Ebin Raja Merly, and S. Kavi tha. "Stolarsky-3 Mean Labeling on Triangular Snake Graphs." International Journal of Mathematics Trends and Technology 53, no. 2 (2018): 150–57. http://dx.doi.org/10.14445/22315373/ijmtt-v53p518.

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17

T. Christy, Et al. "A Study on Sum Divisor Cordial Labeling Graphs." International Journal on Recent and Innovation Trends in Computing and Communication 11, no. 9 (2023): 3394–401. http://dx.doi.org/10.17762/ijritcc.v11i9.9547.

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Cordial labeling refers to a graph with vertices and edges as a sum divisor if there exists a bijection function such that for each edge assign the label 1 , if and 0 otherwise, satisfying the condition is the number of edges having the label 1 , and is the number of edges having the label 0 . A graph with sum-divisor cordial labeling is called a sum-divisor cordial graph. In the paper, we establish this alternate triangular belt graph, twig graph, duplication of the top vertex Alternate triangular snake graph, duplication of top vertex Pentagon snake graph, jellyfish when and are even, Spider

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18

Soleha, M., Purwanto, and D. Rahmadani. "Edge odd graceful of alternate snake graphs." Journal of Physics: Conference Series 2157, no. 1 (2022): 012002. http://dx.doi.org/10.1088/1742-6596/2157/1/012002.

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Abstract Let G be a graph with vertex set V(G), edge set E(G), and the number of edges q. An edge odd graceful labeling of G is a bijection f : E(G) → {1,3,5, …,2q − 1} so that induced mapping f + : V(G) → {0,1,2, …,2q − 1} given by f +(x) = ∑ xy∈E(G) f(xy) (mod 2q) is injective. A graph which admits an edge odd graceful labeling is called edge odd graceful. An alternate triangular snake graph A ( C 3 m ) is a graph obtained from a path u 1 u 2 u 3 … u 2m by joining every u 2i−1 and u 2i to a new vertex υi , 1 ≤ i ≤ m. An alternate quadrilateral snake graph A ( C 4 m ) is a graph obtained from

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19

Kaviya, S., G. Mahadevan, and C. Sivagnanam. "Generalizing TCCD-Number For Power Graph Of Some Graphs." Indian Journal Of Science And Technology 17, SPI1 (2024): 115–23. http://dx.doi.org/10.17485/ijst/v17sp1.243.

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Objective: Finding the triple connected certified domination number for the power graph of some peculiar graphs. Methods: A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found and then proved the upper bound and lower bound of were eq

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20

S, Kaviya, Mahadevan G, and Sivagnanam C. "Generalizing TCCD-Number For Power Graph Of Some Graphs." Indian Journal of Science and Technology 17, SP1 (2024): 115–23. https://doi.org/10.17485/IJST/v17sp1.243.

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Abstract <strong>Objective:</strong> Finding the triple connected certified domination number for the power graph of some peculiar graphs. <strong>Methods:</strong> A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found

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21

M. I. Bosmia, V. R. Visavaliya, and B. M. Patel. "Further Results on Sum Cordial Graphs." Malaya Journal of Matematik 3, no. 02 (2015): 175–81. http://dx.doi.org/10.26637/mjm302/006.

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22

Mahalank, Pushpalatha, Bhairaba Kumar Majhi, and Ismail Naci Cangul. "Some Topological Indices of Double Square Snake Graphs." Nepali Mathematical Sciences Report 38, no. 1 (2021): 8–15. http://dx.doi.org/10.3126/nmsr.v38i1.38872.

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In many areas of science, lattice structures are very useful phenomenons. In network sciences, in chemistry and in social sciences, we face them in the solution of many daily life problems. Several large lattice structures can also be thought as graphs and in that way, are useful in the study of large networks. A very recently defined and studied class of such networks are snake graphs which has close relations with number theory due to the use of continued fractions. Following the works on square snake graphs, in this work, we study some non-Zagreb type topological graph indices of some inter

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23

A. Anat Jaslin Jini. "Relatively Prime Domination Number in Quadrilateral Snake Graphs." Communications on Applied Nonlinear Analysis 32, no. 3s (2024): 154–62. https://doi.org/10.52783/cana.v32.2576.

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A set S⊆V is said to be relatively prime dominating set if it is a dominating set with at least two elements and for every pair of vertices u and v in S, (deg⁡(u),deg⁡〖(v))〗=1. The minimum cardinality of a relatively prime dominating set is called relatively prime domination number and it is denoted by γ_rpd (G). If there is no such pair exist, then γ_rpd (G)=0. For a finite undirected graph G(V,E) and a subset V, the switching of G by is defined as the graph (V, ) which is obtained from G by removing all edges between and its complement V- and adding as edges all non-edges between and V- . Th

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24

M.Kaaviya, Shree, and K.Sharmilaa. "Power-3 Heronian Mean Labeling of Graphs." International Journal of Engineering and Advanced Technology (IJEAT) 9, no. 4 (2020): 1359–61. https://doi.org/10.35940/ijeat.D7831.049420.

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Let be an undirected graph having vertices and edges. Now, defining a function say, is called Power-3 Heronian Mean Labeling of a graph if we could able to label the vertices with dissimilar elements from such that it induces an edge labeling defined as, is dissimilar for all the edges (i,e.) It intimates that the dissimilar vertex labeling induces a dissimilar edge labeling on the graph. The graph which owns Power-3 Heronian Mean Labeling is called an Power-3 Heronian Mean Graph. In this, we have advocated the Power-3 Heronian Mean Labeling of some standard graphs like Path, Comb, Caterpillar

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25

K., Thirusangu, and Selvaganapathy A. "Gaussian anti magic labeling in sunlet and triangular snake graphs." Malaya Journal of Matematik S, no. 1 (2020): 148–52. http://dx.doi.org/10.26637/mjm0s20/0028.

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26

Ismael, Wilma S., Hounam B. Copel, and Sisteta U. Kamdon. "CHROMATIC POLYNOMIALS OF n-CENTIPEDE AND TRIANGULAR SNAKE TSn GRAPHS." Advances and Applications in Discrete Mathematics 36 (November 28, 2022): 1–9. http://dx.doi.org/10.17654/0974165823001.

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27

Evangelista, John Russel D., Hounam B. Copel, Mercedita A. Langamin, Nurijam Hanna M. Mohammad, Sisteta U. Kamdon, and Alcyn R. Bakkang. "GEODETIC POLYNOMIALS OF n-SUNLET AND TRIANGULAR SNAKE TS_n GRAPHS." Advances and Applications in Discrete Mathematics 40, no. 2 (2023): 177–86. http://dx.doi.org/10.17654/0974165823064.

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28

Kalaiselvi, J., and D. Vijayalakshmi. "On Radio k-Chromatic Number of Various Graphs." Indian Journal Of Science And Technology 17, no. 42 (2024): 4415–21. http://dx.doi.org/10.17485/ijst/v17i42.3084.

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Objective: The main objective of the study is to reduce radio spectrums without any interference. This study aims to find the smallest span of radio k chromatic number of various graphs. The minimal number of colors essential to color a graph is called its span. Methods: In this paper, we address the issue of minimizing interference by modeling it as a radio k-coloring problem on graphs, when vertices and the connections between them represent the spectrum bandwidth indicated by edges. For a positive integer k, a radio k – coloring of simply connected graph T, is a function 𝜙: V(T) →{c0, c1, c

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29

M., I. Moussa, and Badr E.M. "LADDER AND SUBDIVISION OF LADDER GRAPHS WITH PENDANT EDGES ARE ODD GRACEFUL." International Journal on Applications of Graph Theory in Wireless Ad hoc Networks and Sensor Networks(GRAPH-HOC) 8, no. 1 (2019): 1–8. https://doi.org/10.5281/zenodo.3351927.

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The ladder graph plays an important role in many applications as Electronics, Electrical and Wireless communication areas. The aim of this work is to present a new class of odd graceful labeling for the ladder graph. In particular, we show that the ladder graph Ln with m-pendant Ln  mk1 is odd graceful. We also show that the subdivision of ladder graph Ln with m-pendant S(Ln)  mk1 is odd graceful. Finally, we prove that all the subdivision of triangular snakes ( k   snake ) with pendant edges 1 ( ) k S snake mk    are odd graceful.

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30

Zalzabila, Lutfiah Alifia, Diari Indriati, and Titin Sri Martini. "EDGE IRREGULAR REFLEXIVE LABELING ON ALTERNATE TRIANGULAR SNAKE AND DOUBLE ALTERNATE QUADRILATERAL SNAKE." BAREKENG: Jurnal Ilmu Matematika dan Terapan 17, no. 4 (2023): 1941–48. http://dx.doi.org/10.30598/barekengvol17iss4pp1941-1948.

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Let G in this paper be a connected and simple graph with set V(G) which is called a vertex and E(G) which is called an edge. The edge irregular reflexive k-labeling f on G consist of integers {1,2,3,...,k_e} as edge labels and even integers {0,2,4,...,2k_v} as the label of vertices, k=max{k_e,2k_v}, all edge weights are different. The weight of an edge xy in G represented by wt(xy) is defined as wt(xy)= f (x)+ f (xy)+ f (y). The smallest k of graph G has an edge irregular reflexive k-labeling is called the reflexive edge strength, symbolized by res (G). In article, we discuss about edge irregu

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31

T. Christy. "An Application on Harmonic Mean Labeling of Variations in Triangular Snake Graphs." Communications on Applied Nonlinear Analysis 31, no. 2 (2024): 11–21. http://dx.doi.org/10.52783/cana.v31.509.

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A graph G with p vertices and q edges is called a harmonic mean(HM) labeling if it is possible to label the vertices x∈v with distinct labels ρ(x) from {1,2,⋯,q+1} in such a way that each edge e=ab is labeled with ρ(ab)=⌈(2ρ(a)ρ(b))/(ρ(a)+ρ(b))⌉ or ⌊(2ρ(a)ρ(b))/(ρ(a)+ρ(b))⌋ then the edge labels are distinct.In this case ρ is called Harmonic mean(HM) labeling of G. In this paper we introduce new graphs obtained from triangular snake graph TS_n such as TS_n∘K_1, and prove that they are Harmonic Mean labeling graphs.

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32

G, Vembarasi, and Gowri R. "Super Root Cube of Cube Difference Labeling of Some Special Graphs." Indian Journal of Science and Technology 14, no. 35 (2021): 2778–83. https://doi.org/10.17485/IJST/v14i35.1336.

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Abstract <strong>Background/Objectives:</strong> This study gives an extended and the new kinds of super root cube of cube difference labeling of some graphs are obtained. <strong>Methods/ Findings:</strong> We derive super root cube of cube difference labeling of path related graph and analyzed cycle related graphs. <strong>Keywords:</strong> Triangular Snake T_n; Cycle graph C_n; Crown C_n©K_1; pendent edge to both sides of each vertex of a path Pn; supr root cube of cube difference labeling of graphs.  

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33

MAHALANK, PUSHPALATHA, BHAIRABA K. MAJHI, and ISMAIL NACI CANGUL. "Several Zagreb indices of double square snake graphs." Creative Mathematics and Informatics 30, no. 2 (2021): 181–88. http://dx.doi.org/10.37193/cmi.2021.02.08.

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34

W., K. M. Indunil, N. Kaluarachchi K., and C. G. Perera A. "k - Odd Prime Labeling of m×n Grid Graphs." Iconic Research and Engineering Journals 6, no. 6 (2022): 7. https://doi.org/10.5281/zenodo.7439763.

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Graph labeling can be mentioned as one of the most prominent research areas in graph theory and the history of graph labeling can be traced back to the 1960s as well. There is a  quite number of graph labeling techniques such as graceful labeling, radio labeling, antimagic labeling, prime labeling, and lucky labeling. There are various subtypes of prime labeling including odd prime labeling, k- prime labeling, neighborhood prime labeling, and coprime labeling. In this study, we explore one of the prime labeling varieties called odd prime labeling. There is a well-known conjecture related

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35

J, Kalaiselvi, and Vijayalakshmi D. "On Radio k-Chromatic Number of Various Graphs." Indian Journal of Science and Technology 17, no. 42 (2024): 4415–21. https://doi.org/10.17485/IJST/v17i42.3084.

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Abstract <strong>Objective:</strong> The main objective of the study is to reduce radio spectrums without any interference. This study aims to find the smallest span of radio k chromatic number of various graphs. The minimal number of colors essential to color a graph is called its span. <strong>Methods:</strong> In this paper, we address the issue of minimizing interference by modeling it as a radio k-coloring problem on graphs, when vertices and the connections between them represent the spectrum bandwidth indicated by edges. For a positive integer k, a radio k – colorin

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36

R N, Rajalekshmi, and Kala R. "GROUP MEAN CORDIAL LABELING OF SOME QUADRILATERAL SNAKE GRAPHS." Journal of the Indonesian Mathematical Society 30, no. 3 (2024): 374–84. http://dx.doi.org/10.22342/jims.30.3.1210.374-384.

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Let G be a (p, q) graph and let A be a group. Let f : V (G) −→ A be a map. For each edge uv assign the label [o(f (u))+o(f (v)) / 2]. Here o(f (u)) denotes the order of f (u) as an element of the group A. Let I be the set of all integerslabeled by the edges of G. f is called a group mean cordial labeling if the following conditions hold: (1) For x, y ∈ A, |vf (x) − vf (y)| ≤ 1, where vf (x) is the number of vertices labeled with x. (2) For i, j ∈ I, |ef (i) − ef (j)| ≤ 1, where ef (i) denote the number of edges labeled with i. A graph with a group mean cordial labeling is called a group mean c

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Barasara, C. M., and Y. B. Thakkar. "DIVISOR CORDIAL LABELING FOR SOME SNAKES AND DEGREE SPLITTING RELATED GRAPHS." South East Asian J. of Mathematics and Mathematical Sciences 19, no. 01 (2023): 211–24. http://dx.doi.org/10.56827/seajmms.2023.1901.17.

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For a graph G = (V (G),E(G)), the vertex labeling function is defined as a bijection f : V (G) → {1, 2, . . . , |V (G)|} such that an edge uv is assigned the label 1 if one f(u) or f(v) divides the other and 0 otherwise. f is called divisor cordial labeling of graph G if the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. In 2011, Varatharajan et al. [24] have introduced divisor cordial labeling as a variant of cordial labeling. In this paper, we study divisor cordial labeling for triangular snake and quadrilateral snake. Moreover, we investigate divi

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Hausawi, Yasser M., Zaid Alzaid, Olayan Alharbi, Badr Almutairi, and Basma Mohamed. "COMPUTING THE SECURE CONNECTED DOMINANT METRIC DIMENSION PROBLEM OF CLASSES OF GRAPHS." Advances and Applications in Discrete Mathematics 42, no. 3 (2025): 219–33. https://doi.org/10.17654/0974165825015.

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This paper investigates the NP-hard problem of finding the lowest secure connected domination metric dimension of graphs. If each vertex in can be uniquely recognized by its vector of distances to the vertices in Scddim, then every vertex set Scddim of a connected graph resolves . If the subgraph induced by Scddim is a nontrivial connected subgraph of , then the resolving set Scddim of is connected. That resolving set is dominating if each vertex in that is not an element of Scddim is a neighbor of some vertices in Scddim. If there is a in such that is a dominating set for any in , then the do

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Rajpal, Singh*1 R.Ponraj2 &. R.Kala3. "3-PRIME CORDIAL LABELING OF SOME CYCLE RELATED SPECIAL GRAPHS." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 5, no. 6 (2018): 98–104. https://doi.org/10.5281/zenodo.1287720.

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Let G be a (p,q) graph. Let f : V(G) ⇾ {1,2,…k}  be a function. For each edge <em>uv</em>, assign the label gcd (f(u),f(v)).  F  is called k-prime cordial labeling of G if | v<sub>f</sub>(i) - v<sub>f</sub>(j) |<strong> ≤ </strong>1, i,j  ∊ {1,2,…k}, and   | e<sub>f</sub>(0) - e<sub>f</sub>(1) |<strong> ≤ </strong>1 where v<sub>f</sub>(x)  denotes the number of vertices labeled with x, e<sub>f</sub>(1)   and   e<sub>f</sub>(0) respectively the number of edges labeled with 1 and not labeled with 1. A graph which admits a

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kumar, Nand kishor, and Priti Singh. "Symmetry in the context of the strongly ⋆- graph, Cube Difference Labeling graph, Triangular Snake graph, and Theta graph." Journal of Scientific Research 67, no. 04 (2023): 52–57. http://dx.doi.org/10.37398/jsr.2023.670409.

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This paper presents the findings of a brief history of graph theory as well as an outline of the theory itself. This page discusses the strongly-graph, the cube difference labeling graph, the triangular snake graph, and the theta graph. In addition, we define them, present a formula, and explain the symmetrical relationship that exists between these graphs. Include some new graph families in your explanation, as well as examples and drawings.

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Rahmayanti, Sri, Valdo E. Pasaribu, Sawaluddin Nasution, and Sishi Liani Salnaz. "Exponent and scrambling index of double alternate circular snake graphs." IOP Conference Series: Materials Science and Engineering 300 (January 2018): 012079. http://dx.doi.org/10.1088/1757-899x/300/1/012079.

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Ponraj, R., J. X. V. Parthipan, and R. Kala. "A Note on Pair Sum Graphs." Journal of Scientific Research 3, no. 2 (2011): 321–29. http://dx.doi.org/10.3329/jsr.v3i2.6290.

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Let G be a (p,q) graph. An injective map ƒ: V (G) →{±1, ±2,...,±p} is called a pair sum labeling if the induced edge function, ƒe: E(G)→Z -{0} defined by ƒe (uv)=ƒ(u)+ƒ(v) is one-one and ƒe(E(G)) is either of the form {±k1, ±k2,…, ±kq/2} or {±k1, ±k2,…, ±k(q-1)/2} {k (q+1)/2} according as q is even or odd. Here we prove that every graph is a subgraph of a connected pair sum graph. Also we investigate the pair sum labeling of some graphs which are obtained from cycles. Finally we enumerate all pair sum graphs of order ≤ 5.Keywords: Cycle; Path; Bistar; Complete graph; Complete bipartite graph;

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Jeyanthi, P., and K. Jeya Daisy. "Zk-Magic labeling of subdivision graphs." Discrete Mathematics, Algorithms and Applications 08, no. 03 (2016): 1650046. http://dx.doi.org/10.1142/s1793830916500464.

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For any nontrivial abelian group [Formula: see text] under addition a graph [Formula: see text] is said to be [Formula: see text]-magic if there exists a labeling [Formula: see text] such that the vertex labeling [Formula: see text] defined as [Formula: see text] taken over all edges [Formula: see text] incident at [Formula: see text] is a constant. An [Formula: see text]-magic graph [Formula: see text] is said to be [Formula: see text]-magic graph if the group [Formula: see text] is [Formula: see text] the group of integers modulo [Formula: see text]. These [Formula: see text]-magic graphs ar

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R., Sivakumar, and Paulraj M.S. "Triple Connected Roman Domination Number on Some Particular Graphs." International Journal of Innovative Science and Research Technology 7, no. 6 (2022): 252–57. https://doi.org/10.5281/zenodo.6757884.

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On a graph G, we can define a Roman domination function 𝒇:𝑽 → {𝟎, 𝟏, 𝟐} satisfying the condition that every vertex 𝒖 ∈ 𝑽for which 𝒇(𝒖) = 𝟎 is adjacent to at least one vertex 𝒗 ∈ 𝑽for which𝒇(𝒗) = 𝟐 . The weight of a Roman dominating function is the value𝒇(𝒗) = ∑ 𝒇(𝒗) 𝒗∈𝑽 . The Roman domination number 𝜸𝑹(𝑮) is the minimum weight of a Roman dominating function on 𝑮. In a Roman dominating function if the induced subgraph 〈𝑽𝟏 ∪ 𝑽𝟐 〉 𝒐𝒓 〈𝑽𝟐 〉 is triple connected, then the Roman dominating function is called triple connected Roman dominating function (TCRDF) In this paper,

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Et al., P. K. Hemalatha. "A Modified Fuzzy Labeling Graph using Geometric Mean and Harmonic mean and its Application." Advances in Nonlinear Variational Inequalities 26, no. 2 (2023): 15–35. http://dx.doi.org/10.52783/anvi.v26.i2.252.

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The Modified Fuzzy Labeling Graph (MFLG) has gained popularity in the field of image processing due to its ability to accurately represent complex images. However, there are limitations to the MFLG approach that can be addressed through the use of geometric mean and harmonic measures. In this paper, the authors propose a new idea on a modified fuzzy labeling graph. A Modified fuzzy (M ) graph σ is a function from V to [0,1] and µ is a function from E to [0,1] where ∀ . The modified fuzzy labeling has an edge value, which is less than or equal to the maximum of two endpoints that is To obtain t

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Ponraj, R., K. Annathurai, and R. Kala. "Some results on 4- remainder cordial labeling of graphs." Ars Combinatoria 162 (March 30, 2025): 39–49. https://doi.org/10.61091/ars162-04.

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Let \(G\) be a \((p,q)\) graph. Let \(f\) be a function from \(V(G)\) to the set \(\{1,2,\ldots, k\}\) where \(k\) is an integer \(2< k\leq \left|V(G)\right|\). For each edge \(uv\) assign the label \(r\) where \(r\) is the remainder when \(f(u)\) is divided by \(f(v)\) (or) \(f(v)\) is divided by \(f(u)\) according as \(f(u)\geq f(v)\) or \(f(v)\geq f(u)\). \(f\) is called a \(k\)-remainder cordial labeling of \(G\) if \(\left|v_{f}(i)-v_{f}(j)\right|\leq 1\), \(i,j\in \{1,\ldots , k\}\) where \(v_{f}(x)\) denote the number of vertices labeled with \(x\) and \(\left|\eta_{e}(0)-\eta_{o}(1)

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Manamtam, J. A., A. D. Garciano, and M. A. C. Tolentino. "Sigma chromatic numbers of the middle graph of some families of graphs." Journal of Physics: Conference Series 2157, no. 1 (2022): 012001. http://dx.doi.org/10.1088/1742-6596/2157/1/012001.

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Abstract Let G be a nontrivial connected graph and let c : V (G) → ℕ be a vertex coloring of G, where adjacent vertices may have the same color. For a vertex υ of G, the color sum σ(υ) of υ is the sum of the colors of the vertices adjacent to υ. The coloring c is said to be a sigma coloring of G if σ(u) ≠ σ(υ) whenever u and υ are adjacent vertices in G. The minimum number of colors that can be used in a sigma coloring of G is called the sigma chromatic number of G and is denoted by σ(G). In this study, we investigate sigma coloring in relation to a unary graph operation called middle graph. W

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Kraposhin, V. S., A. L. Talis, V. G. Kosushkin, A. A. Ogneva, and L. I. Zinober. "Structures of the cubic and rhombohedral high-pressure modifications of silicon as packing of the rod-like substructures determined by the algebraic geometry." Acta Crystallographica Section B Structural Science 64, no. 1 (2008): 26–33. http://dx.doi.org/10.1107/s0108768107059800.

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Tessellations by generating clusters are proposed for the high-pressure phases BC8 and R8 of silicon. The structures of both high-pressure phases are represented by the parallel packings of rods. The latter are stacks of distorted icosahedra, joined by a common triangular face and flattened out along the threefold symmetry axis. Along the rod axis there is an alternation of empty and double-centered icosahedra. The empty icosahedra are additionally distorted in the cubic BC8 phase by antiparallel rotation about the rod axis, while the double-centered icosahedra are distorted by that rotation i

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Baskaran, Thamaraiselvi, and Rajasekaran Ganapathy. "A Study on C -Exponential Mean Labeling of Graphs." Journal of Mathematics 2022 (October 7, 2022): 1–7. http://dx.doi.org/10.1155/2022/2865573.

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A function h is mentioned as a C -exponential mean labeling of a graph G V , E that has s vertices and r edges if h : V G ⟶ 1 , 2 , 3 , ⋯ , r + 1 is injective and the generated function h ∗ : E G ⟶ 2 , 3 , 4 , ⋯ , r + 1 defined by h ∗ a b = 1 / e h b h b / h a h a 1 / h b − h a , for all a b ∈ E G , is bijective. A graph which recognizes a C -exponential mean labeling is defined as C -exponential mean graph. In the following study, we have studied the exponential meanness of the path, the graph triangular tree of T n , C m P n , cartesian product of two paths P m ▫ P n , one-sided step graph o

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Zeen El Deen, Mohamed R. "Edge δ− Graceful Labeling for Some Cyclic-Related Graphs". Advances in Mathematical Physics 2020 (20 січня 2020): 1–18. http://dx.doi.org/10.1155/2020/6273245.

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In this paper, we introduce a new type of labeling of a graph G with p vertices and q edges called edge δ− graceful labeling, for any positive integer δ, as a bijective mapping f of the edge set EG into the set δ,2δ,3δ,⋯,qδ such that the induced mapping f∗:VG→0,δ,2δ,3δ,⋯,qδ−δ, given by f∗u=∑uv∈EGfuvmodδk, where k=maxp,q, is an injective function. We prove the existence of an edge δ− graceful labeling, for any positive integer δ, for some cycle-related graphs like the wheel graph, alternate triangular cycle, double wheel graph Wn,n, the prism graph Πn, the prism of the wheel PWn, the gear graph

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