Open Access

L. Merrit anisha, M. Regees and T. Nicholas

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A graph $G=(V,E)$ with $p$ vertices and $q$ edges is said to be edge bimagic harmonious if there exists a bijection $f:V\cup E \rightarrow \{1, 2, 3,…,p+q\}$ such that for each edge $xy$ in $E(G)$, the value of $[(f(x) + f(y))(mod\ q) + f(xy)]$ is equal to $k_1$ or $k_2$, where $k_1$ and $k_2$ are two distinct magic constants. In this paper we prove that the $\left\langle B_{m,n}:2\right\rangle$, restricted square graph of $B_{n,n}$ and duplication of apex vertex of $B_{n,n}$ are edge bimagic harmonious graphs.

Keywords:
Graph, Bijection, Harmonious, Labeling, Magic, Bimagic, Bistar graphs.