Abstract
For a graph, a function is called an edge product cordial labeling of G, if the induced vertex labeling function is defined by the product of the labels of the incident edges as such that the number of edges with label 1 and the number of edges with label 0 differ by at most 1 and the number of vertices with label 1 and the number of vertices with label 0 differ by at most 1. In this paper, we show that the graphs obtained by duplication of a vertex, duplication of a vertex by an edge or duplication of an edge by a vertex in a crown graph are edge product cordial. Moreover, we show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We also show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial.
Highlights
We begin with a simple, finite, undirected graph G = (V (G), E (G)) where V (G)and E (G) denote the vertex set and the edge set respectively
The graph obtained by duplication of an arbitrary vertex of the cycle in a crown graph is an edge product cordial graph
The graph obtained by duplication of an arbitrary vertex of the cycle by a new edge in a crown graph is edge product cordial graph
Summary
We show that the graph obtained by duplication of each of the vertices of degree three by an edge in a gear graph is edge product cordial. We show that the graph obtained by duplication of each of the pendent vertices by a new vertex in a helm graph is edge product cordial. The graph obtained by duplication of an arbitrary vertex of the cycle in a crown graph is an edge product cordial graph.
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