Cordial labeling of mK(n)

Abstract

Suppose G = (V,E) is a graph with vertex set V and edge set E. A vertex labeling f: V --> (0, 1) induces an edge labeling f*: E --> (0, 1) defined by f*(ny) = If(x)- f(y)l. For i is an element of (0, 1), let v(f)(i) and e(f)(i) be the number of vertices v and edges e with f(v) = i and f*(e) = i, respectively. A graph G is cordial if there exists a vertex labeling f such that v(f)(0) - v(f)(1)less than or equal to 1 and e(f)(0) - e(f)(1) less than or equal to 1. This paper determines all m and n for which mK(n) is cordial.