SUPER-EDGE MAGIC TOTAL LABELING IN CERTAIN CLASSES OF GRAPHS

Abstract

Duplicate graph of a graph is constructed from a graph with vertex set $V$ of $p$ vertices and edge set $E$ of $q$ edges as a new graph with vertex set union of $V, V'$ where $V'$ is a set disjoint with $V$ having $p$ vertices such that $uv$ is an edge in the graph $G$ if and only if $uv'$ and $u'v$ are the edges in its duplicate graph. Super-edge magic total labeling of a graph is a bijection which labels the vertices with integers 1 to p and edges with integers $p+1$ to $p+q$ such that the induced edge sum of edges defined as ``sum of labels of end vertices and label of that edge" are all same. In this paper, we provide algorithms and prove existence of super-edge magic total labeling in extended duplicate graphs of twig, comb, star and bi-star graphs.