Abstract
For a graph having no isolated vertex, a function is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex is such that the number of edges with label 0 and the number of edges with label 1 differ by at most 1 and the number of vertices with label 0 and the number of vertices with label 1 also differ by at most 1. In this paper, we discuss edge product cordial labeling for some cycle related graphs.
Highlights
We begin with simple, finite, undirected graph G = (V (G), E (G)) having no isolated vertex where V (G) and E (G) denote the vertex set and the edge set respectively, v (G) and E (G) denote the number of vertices and edges respectively
For a graph G = (V (G), E (G)) having no isolated vertex, a function f : E (G) → {0,1} is called an edge product cordial labeling of graph G, if the induced vertex labeling function defined by the product of labels of incident edges to each vertex is such that the number of edges with label 0 and the number of edges with label 1 differ by at most 1 and the number of vertices with label 0 and the number of vertices with label 1 differ by at most 1
Finite, undirected graph G = (V (G), E (G)) having no isolated vertex where V (G) and E (G) denote the vertex set and the edge set respectively, v (G) and E (G) denote the number of vertices and edges respectively
Summary
We consider the following two cases: Case 1: If n is odd, define the mapping g : E (G) → {0,1} in order to satisfy edge condition for edge product cordial graph it is essential to assign label 0 to 3n edges out of 6n edges.
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