Super edge-magic deficiency of join-product graphs
Abstract
A graph G is called super edge-magic if there exists a bijective function f from V(G)UE(G) to {1,2,...,|V(G) U E(G)|} such that f(V(G)) = {1,2,..., \V(G)\} and f(x) + f(xy) + f(y) is a constant k for every edge xy of G. Furthermore, the super edge-magic deficiency of a graph G is either the minimum nonnegative integer n such that G U nK1 is super edge-magic or +∞ if there exists no such integer. Join product of two graphs is their graph union with additional edges that connect all vertices of the first graph to each vertex of the second graph. In this paper, we study the super edge-magic deficiencies of a wheel minus an edge and join products of a path, a star, and a cycle, respectively, with isolated vertices. In general, we show that the join product of a super edge-magic graph with isolated vertices has finite super edge-magic deficiency. © 2017 Utilitas Mathematica Publishing Inc.. All rights reserved.
