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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     author = {M. Imran and A. Q. Baig and A. S. Fe\v{n}ov\v{c}{\'\i}kov\'a},
     title = {Some {Results} on {Super} {Edge-Magic} {Deficiency} of {Graphs}},
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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/