On the cordiality of the t-uniform homeomorphs -: II (Complete graphs)

Let G be a simple graph with vertex set V and edge set E. A vertex labeling f : V --> {0,1} induces an edge labelling (f) over bar : E --> {0,1} defined by (f) over bar (uv) =\ f(u) - f(v)\. Let v(f)(0), v(f)(1) denote the number of vertices v with f(v) = 0 and f(v) = 1 respectively. Let e(f)(0), e(f)(1) be similarly defined. A graph is said to be 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. A t-uniform homeomorph P-t(G) of G is the graph obtained by replacing all edges of G by vertex disjoint paths of length t. In this paper we show that (1) P-t(K-2n) is cordial for all t greater than or equal to 2. (2) P-t(K2n+1) is cordial iff (a) t equivalent to 0( mod 4) OR (b) t is odd and n is not equivalent to 2( mod 4) OR (c) t equivalent to 2( mod 4) and n is even.