On Super Magic Algorithm for Union of Comb and Star Graph

Authors : Rongbing HUANG, Muhammad Farhan HANİF, Muhammad Kamran SİDDİQUİ, Muhammad Faisal NADEEM

Pages : 82-89

View : 12 | Download : 13

Publication Date : 2023-04-30

Article Type : Research Paper

Abstract :In [7], Enomoto \\emph{et al.} identified the concept of super edge magic total labeling of graphs by getting motivation from the idea of edge-magic labeling of graphs that was brought into light by Kotzig and Rosa [20]. An edge magic total labeling of a graph $G$ is a one to one map $\\phi$ from $Vinsert ignore into journalissuearticles values(G);\\cup Einsert ignore into journalissuearticles values(G);$ onto the set $ \\{1, 2, \\dots , |Vinsert ignore into journalissuearticles values(G);|+|Einsert ignore into journalissuearticles values(G);|\\}$ with the property that, there is an integer constant $\\alpha$ such that $\\phiinsert ignore into journalissuearticles values(u);+\\phiinsert ignore into journalissuearticles values(uv);+\\phiinsert ignore into journalissuearticles values(v);=\\alpha$ for any $insert ignore into journalissuearticles values(u,v);\\in Einsert ignore into journalissuearticles values(G);.$ Moreover if $\\phiinsert ignore into journalissuearticles values(Vinsert ignore into journalissuearticles values(G););=\\{1, 2, \\dots , |Vinsert ignore into journalissuearticles values(G);|\\}$, then edge magic total labeling is called super edge magic total labeling. In this paper, we study the super edge magic total labeling of generalized comb graph.
Keywords : magic graph, SEM total labeling, comb graph, star