Geodesic
Some Results on Super Edge-Magic Deficiency of Graphs
Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 237

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

An edge-magic total labeling of a graph $G$ is a bijection $f: \linebreak V(G)\cup E(G)\to \{1, 2, …, |V(G)|+|E(G)|\}$, where there exists a constant $k$ such that $f(u)+f(uv)+f(v)=k$, for every edge $uv\in E(G)$. Moreover, if the vertices are labeled with the numbers $1, 2, …, |V(G)|$ such a labeling is called a super edge-magic total labeling. The super edge-magic deficiency of a graph $G$, denoted by $\mu_s(G)$, is the minimum nonnegative integer $n$ such that $G\cup nK_1$ has a~super edge-magic total labeling or is defined to be $\infty$ if there exists no such $n$. In this paper we study the super edge-magic deficiencies of two types of snake graph and a prism graph $D_n$ for $n\equiv 0\pmod 4$. We also give an exact value of super edge-magic deficiency for a ladder $P_n ×K_2$ with $1$ pendant edge attached at each vertex of the ladder, for $n$ odd, and an exact value of super edge-magic deficiency for a square of a path $P_n$ for $n\ge 3$.
Keywords: super edge-magic total labeling, super edge-magic deficiency, block graph, snake graph, prism, corona of graphs, square of graph 
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     title = {Some {Results} on {Super} {Edge-Magic} {Deficiency} of {Graphs}},
     journal = {Kragujevac Journal of Mathematics},
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M. Imran; A. Q. Baig; A. S. Feňovčíková. Some Results on Super Edge-Magic Deficiency of Graphs. Kragujevac Journal of Mathematics, Tome 44 (2020) no. 2, p. 237 . http://geodesic.mathdoc.fr/item/KJM_2020_44_2_a5/