The corona between cycles and paths

Nada, S.I.; ELrokh, Ashraf; Elsakhawi, E. A.; Sabra, D. E.

doi:10.1016/j.joems.2016.08.004

Cited by 8 publications

(5 citation statements)

References 2 publications

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“…[ 29 ] The corona product of two graphs with vertices and edges and with vertices and edges is defined as the graph obtained by taking one copy of and copies of , and then joining the vertex of with an edge to every vertex in the copy of .…”

Section: Corona Product Of Hypertree and A Pathmentioning

confidence: 99%

Biochemical and phylogenetic networks-I: hypertrees and corona products

et al. 2021

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We have obtained graph-theoretically based topological indices for the characterization of certain graph theoretical networks of biochemical interest. We have derived certain distance, degree and eccentricity based topological indices for various k -level hypertrees and corona product of hypertrees. We have also pointed out errors in a previous study. The validity of our results is supported by computer codes for the respective indices. Several biochemical applications are pointed out.

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Section: Corona Product Of Hypertree and A Pathmentioning

confidence: 99%

Biochemical and phylogenetic networks-I: hypertrees and corona products

et al. 2021

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“…e following three properties are shared by the majority of graph labeling problems: (i) A set of numbers from which to select vertex labels (ii) A rule that gives each edge a labeling (iii) Some rules that these labels must meet A Dynamic Survey of Graph Labeling by Gallian [4] is a complete survey of graph labeling. ere are several contributions and various types of labeling [1,[3][4][5][6][7][8][9][10][11][12][13][14][15]. Graceful labeling and harmonious labeling are two of the major styles of labeling.…”

Section: Introductionmentioning

confidence: 99%

“…Cahit proposed a third major style of labeling, cordial, in 1987 [14], which combines elements of the previous two. e cordiality of the corona between cycles C n and paths P n was investigated by Nada S. et al [8]. is research focuses on graph labeling of this type.…”

Section: Introductionmentioning

confidence: 99%

A Novel Problem to Solve the Logically Labeling of Corona between Paths and Cycles

ELrokh

Al-Shamiri

El-hay

2022

Journal of Mathematics

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In this study, we propose a new kind of graph labeling which we call logic labeling and investigate the logically labeling of the corona between paths P n and cycles C n , namely, P n ⊙ C m . A graph is said to be logical labeling if it has a 0 − 1 labeling that satisfies certain properties. The corona G 1 ⊙ G 2 of two graphs G 1 (with n 1 vertices and m 1 edges) and G 2 (with n 2 vertices and m 2 edges) is defined as the graph formed by taking one copy of G 1 and n 1 copies of G 2 and then connecting the i th vertex of G 1 with an edge to every vertex in the i th copy of G 2 .

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“…Corona product of G and H is the graph G ⊙ H, where G has n vertices, e edges, and H has k vertices, l edges. The graph G ⊙ H is obtained by taking one copy of G and n copies of H and making the ith vertex of G adjacent to every vertex of the ith copy of H, where 1 ≤ i ≤ n. Nada et al [8] investigated the cordiality of Corona between cycles and paths. Ma et al [7] proved that Lexicographic product graphs P m [P n ] are anti-magic.…”

Section: Introductionmentioning

confidence: 99%

A Study of Anti-Magic Graphs on Corona Product of Complete Graphs and Complete Bipartite Graphs

Muya¹,

Shobhalatha²

2022

Comm. Math. Appl.

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Graph labeling has a wide range of applications such as coding theory, X-ray crystallography, network design, and circuit design. It can be done by assigning numbers to edges, vertices or to both. An anti-magic labeling of a graph G is a one-to-one correspondence between the edge set E(G) and the set {1, 2, 3, . . . , |E|} such that the vertex sums are pairwise distinct. The vertex sum is the sum of labels assigned to edges incident to a vertex. Corona product of the graphs H and T is the graph H ⊙ T which is obtained by taking one copy of H and |V (H)| copies of T and making the ith vertex of H adjacent to every vertex of the ith copy of T, 1 ≤ i ≤ |V (H)|. In this study, we prove that the Corona product K n ⊙ K m,m generates anti-magic graphs. We also develop a programme using MATLAB to demonstrate this anti-magic property.

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The corona between cycles and paths

Cited by 8 publications

References 2 publications

Biochemical and phylogenetic networks-I: hypertrees and corona products

Biochemical and phylogenetic networks-I: hypertrees and corona products

A Novel Problem to Solve the Logically Labeling of Corona between Paths and Cycles

A Study of Anti-Magic Graphs on Corona Product of Complete Graphs and Complete Bipartite Graphs

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