Abstract
A graph is said to be a product cordial graph if there exists a function with each edge assign the label , such that the number of vertices with label 0 and the number of vertices with label 1 differ atmost by 1, and the number of edges with label 0 and the number of edges with label 1 differ by atmost 1. We discuss the product cordial labeling of the graphs obtained by duplication of some graph elements of gear graph. Also, we derive some product cordial graphs obtained by vertex switching operation on gear graph.
Highlights
We begin a simple, finite, undirected graph G = (V (G), E (G)), where V (G) andE (G) are vertex set and edge set respectively
The graph obtained by duplication of each vertex of degree two in the gear graph is not a product cordial graph
The graph obtained by duplication of each vertex of degree two by an edge in the gear graph is a product cordial graph
Summary
Product Cordial Labeling, Gear Graph, Duplication, Vertex Switching Let G be the graph obtained from Gn by duplicating each vertex ui of degree two by an edge ui′ui′′ respectively for all i = 1, 2, 3, , n .
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