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Journal articles on the topic 'Triangular Snake Graphs'

Author: Grafiati

Published: 3 June 2025

Last updated: 31 July 2025

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1

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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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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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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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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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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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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7

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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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

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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10

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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11

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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12

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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13

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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14

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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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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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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17

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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18

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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19

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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20

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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21

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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22

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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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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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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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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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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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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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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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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30

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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31

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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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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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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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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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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Jeyanthi, P., and T. Saratha Devi. "Edge Pair Sum Labeling." Journal of Scientific Research 5, no. 3 (2013): 457–67. http://dx.doi.org/10.3329/jsr.v5i3.15001.

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An injective map f : E(G) ? {±1, ±2, ,±q } is said to be an edge pair sum labeling of a graph G(p, q) if the induced vertex function f*:V(G) ? Z {0} defined by f*(?) = ?e?E? f(e) is one-one, where denotes the set of edges in G that are incident with a vertex v and f*(V(G)) is either of the form {±k1, ±k2, , ±kp/2} or {±k1, ±k2, , ±k(p-1)/2}U{kp/2}according as p is even or odd. A graph with an edge pair sum labeling is called an edge pair sum graph. In this paper we prove that path Pn, cycle Cn, triangular snake, PmUK1,n, Cn?Kmc are edge pair sum graphs. Keywords: Pair sum graph, edge pair su

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Mohamed, Basma, and Mohammed Badawy. "Some New Results on Domination and Independent Dominating Set of Some Graphs." Applied and Computational Mathematics 13, no. 3 (2024): 53–57. http://dx.doi.org/10.11648/j.acm.20241303.11.

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One area of graph theory that has been studied in great detail is dominance in graphs. Applications for dominating sets are numerous. In wireless networking, dominant sets are used to find effective paths inside ad hoc mobile networks. They have also been used in the creation of document summaries and safe electrical grid systems. A set &lt;I&gt;S&lt;/I&gt;⊆&lt;I&gt;V&lt;/I&gt; is said to be dominating set of &lt;I&gt;G&lt;/I&gt; if for every &lt;i&gt;v &lt;/i&gt;є &lt;I&gt;V&lt;/I&gt;-&lt;I&gt;S&lt;/I&

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Shanmugavelan, S., and C. Natarajan. "ON HOP DOMINATION NUMBER OF SOME GENERALIZED GRAPH STRUCTURES." Ural Mathematical Journal 7, no. 2 (2021): 121. http://dx.doi.org/10.15826/umj.2021.2.009.

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A subset \( H \subseteq V (G) \) of a graph \(G\) is a hop dominating set (HDS) if for every \({v\in (V\setminus H)}\) there is at least one vertex \(u\in H\) such that \(d(u,v)=2\). The minimum cardinality of a hop dominating set of \(G\) is called the hop domination number of \(G\) and is denoted by \(\gamma_{h}(G)\). In this paper, we compute the hop domination number for triangular and quadrilateral snakes. Also, we analyse the hop domination number of graph families such as generalized thorn path, generalized ciliates graphs, glued path graphs and generalized theta graphs.

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R., Anusuya. "CUBE DIFFERENCE LABELING OF SOME SPECIAL GRAPH FAMILIES." GLOBAL JOURNAL OF ENGINEERING SCIENCE AND RESEARCHES 6, no. 5 (2019): 462–70. https://doi.org/10.5281/zenodo.3229432.

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A new labeling and a new graph called cube difference labeling and the cube difference is defined.  Let G be a (p,q) graph.  G is said to have a cube difference labeling if there exists injection <strong>f:V(G)—&rsaquo;{0,1,2,…,p-1}</strong> such that the edge set of G has assigned a weight defined by the absolute cube difference of its end vertices, the resulting weights are distinct.  A graph which admits cube difference labeling is called cube difference graph.  The cube difference labeling for some special graph families like <strong>Pan graph</strong>, <st

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H, Anitha, Sowjanya S K, B. Shanmukha, and Karthik K R. "K - Power-3 Heronian Mean Labeling of Graphs." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 12, no. 11 (2024). http://dx.doi.org/10.47191/ijmcr/v12i11.04.

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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 Snake related graphs like triangular, alternative triangular and dou

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"Strongly Multiplicative Labeling on subdivision of Triangular Snake & Ladder graphs, Cyclic Quadrilateral & Pentagonal snake graphs." International Journal of Innovative Technology and Exploring Engineering 9, no. 2 (2019): 358–62. http://dx.doi.org/10.35940/ijitee.b6353.129219.

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In this paper we study the specific families of graphs which admit strongly multiplicative labeling. It is proved that the Subdivision of Triangular Snake, Subdivision of Alternate Triangular Snake and Subdivision of Ladder are strongly multiplicative graphs. In this paper it is also established that Cyclic Quadrilateral Snakes admit strongly multiplicative labeling. Also Cyclic Pentagonal Snakes and corona graph of TnΘk2 admit strongly multiplicative labeling. Suitable examples are given to establish the strongly multiplicative labeling on these graphs.

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Imran, Muhammad, Murat Cancan, Yasir Ali, et al. "Some Path Related Cordial Graphs." International Journal of Research Publication and Reviews, October 30, 2022, 2178–84. http://dx.doi.org/10.55248/gengpi.2022.3.10.66.

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In this research paper, we prove that different families of snake graphs such as triangular snake graph with pendant edges, alternate triangular snake graph with and without pendant edges, quadrilateral snake graph with and without pendant edges, alternate quadrilateral snake graph with pendant edges and double quadrilateral snake graph with and without pendant edges are cordial graphs.

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E., M. Badr, and E. Abdel-aal M. "ODD GRACEFULL LABELING FOR THE SUBDIVISON OF DOUBLE TRIANGLES GRAPHS." February 28, 2013. https://doi.org/10.5281/zenodo.1288287.

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The aim of this paper is to present some odd graceful graphs. In particular we show that an odd graceful labeling of the all subdivision of double triangular snakes ( 2∆k -snake ). We also prove that the all subdivision of 2 m∆1 -snake are odd graceful. Finally, we generalize the above two results (the all subdivision of 2 m∆k -snake are odd graceful).

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"Mean Square Cordial Labeling of Some Snake Graphs." International Journal of Innovative Technology and Exploring Engineering 8, no. 9S3 (2019): 473–77. http://dx.doi.org/10.35940/ijitee.i3090.0789s319.

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In this paper we investigate that some snake related graph admits mean square cordial labeling. In particular , mean square cordial labeling of a Triangular snake Tk, Subdivision of a triangular snake S(Tk), Quadrilateral snake QSk, Subdivision of a quadrilateral snake S(QSk ) are discussed.

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Badr, E.M., and B. Mohamed. "A Combinatorial Approach For the Spanning Tree Entropy in Complex Network." May 25, 2019. https://doi.org/10.5281/zenodo.3228704.

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<strong>The goal of this paper is to propose the combinatorial method to facilitate the calculation of the number of spanning trees for complex networks. In particular, we derive the explicit formulas for the triangular snake, double triangular snake, four triangular snake, the total graph of path, the generalized friendship graphs and the subdivision of double triangular snake. Finally, we calculate their spanning trees entropy and we compare it between them.</strong>

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R.Gopi. "F-Root Square Mean Labeling of Some Graphs." May 23, 2019. https://doi.org/10.5281/zenodo.3201726.

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Throughout this paper, by a graph we mean a finite, undirected and simple graph. Let G(V,E) be a graph with p vertices and q edges. For notations and terminology, we follow [3]. For a detailed survey on graph labeling, we refer [2].

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Dr. Puli Latha Devi. "On Some Topological Indices of the Triangular Snake Graph and Alternate Triangular Snake Graph." International Journal of Scientific Research in Science and Technology, July 10, 2023, 241–46. http://dx.doi.org/10.32628/ijsrst52310419.

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The quantitative specifications which are used to narrate the atomic topology of graphs are usually entitled as topological indices in theoretical Chemistry. The features of physical and chemical properties like melting point, entropy, boiling point, energy generation and enthalpy of vaporization of chemical compounds can be estimated by means of these topological indices. The field of Graph theory has a remarkable application of linking certain graphs with many types of topological indices. In this paper we compute first and second Zagreb indices, Randi´c index, sum-connectivity index, harmon

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