Abstract
In this paper we investigate product cordial labeling for some new graphs. We prove that the friendship graph, cycle with one chord (except when n is even and the chord joining the vertices at diameter distance), cycle with twin chords (except when n is even and one of the chord joining the vertices at diameter distance) are product cordial graphs. We also investigated middle graph of path $P_{n}$ admits product cordial labeling.
Highlights
We begin with finite, connected and undirected graph G = (V(G), E(G)) without loops and multiple edges
The present paper is aimed to investigate some results on product cordial labeling in which absolute difference is replaced by product of the vertex labels
In present investigations we prove that the friendship graph, cycle with one chord, cycle with twin chords and middle graph of path are product cordial graphs
Summary
Definition 1.3 A binary vertex labeling of graph G is called cordial labeling if |v f (0) − v f (1)| ≤ 1 and |e f (0) − e f (1)| ≤ 1. The present paper is aimed to investigate some results on product cordial labeling in which absolute difference is replaced by product of the vertex labels. Definition 1.4 A binary vertex labeling of graph G with induced edge labeling f ∗ : E(G) → {0, 1} defined by f ∗(e = uv) = They proved that a graph with p vertices and q edges with p ≥ 4 is product cordial q
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