Abstract
We proved that Pn+1m is total product cordial. We also give sufficient conditions for the graph to admit (or not admit) a product cordial labeling.
Highlights
Let G(V, E) denote a simple and finite connected graph G with vertex set V and edge set E
We proved that Pnm+1 is total product cordial
Let Vf(i) and ef∗(i) denote the number of vertices and edges labeled with i ∈ {0, 1}
Summary
Let G(V, E) denote a simple and finite connected graph G with vertex set V and edge set E. Suppose f and f∗ denote a vertex and an edge labeling of a graph, respectively. A graph G is called a product cordial graph if it admits a product cordial labeling. A graph G is called a total product cordial graph if it admits a total product cordial labeling. Sundaram et al [4, 5] proved that graphs are total product cordial: every product cordial graph of even order or odd order and even size; trees; all cycles except C4; Kn,2n−1; Cn with m edges appended at each vertex; fans; wheels; helms. In [6], Ramanjaneyulu et al proved that a family of planar graphs for which each face is a 4-cycle admit a total product cordial labeling. The degree of a vertex u, denoted by d(u) (or d), is the number of edges incident to u
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