Super Edge-magic Total Labeling of Combination Graphs

EasyChair Preprint no. 1511

Abstract

A $(p,q)$ graph $G$ has edge-magic total labeling if there exists a bijective function $f$: $V(G)\cup E(G) \to \{1,2,...,p+q\}$, such that $ f(u) + f(v) + f(uv) = k $ is a constant for any edge $uv$ of $G$. Moreover, $G$ is said to be super edge-magic total labeling graph if $f(V(G)) =\{1, 2, ..., p\}$. In this paper, we introduce a new operation $\bigtriangleup$ called generalized coalescence, then we investigate super edge-magic total labeling of composite graph $F_m \bigtriangleup F_n\bigtriangleup C_i \bigtriangleup S_j $ which has four components. Finally, by giving some specific labels, we prove that for any $i$ and $j$ with $3 \le i \le 7$ and $j \ge 2$ both $F_3 \bigtriangleup F_2\bigtriangleup C_i \bigtriangleup S_j $ and $F_3 \bigtriangleup F_3\bigtriangleup C_i \bigtriangleup S_j $ are super edge-magic total labeling graphs.

Keyphrases: composite graph., generalized coalescence, super edge-magic total labeling

@Booklet{EasyChair:1511,
  author = {Jingwen Li and Bimei Wang and Yanbo Gu and Shuhong Shao},
  title = {Super Edge-magic Total Labeling of Combination Graphs},
  howpublished = {EasyChair Preprint no. 1511},

  year = {EasyChair, 2019}}