On k-cordiality of cycles, crowns and wheels

摘要

A graph G is called A-cordial if there is a vartex labeling f of G with elements from A, where A is an abelian group, such that |υα-υb|≤1 for all a, b∈A, in which υa denotes the number of vertices labelled a, and the induced edge labeling defined by f (uυ) =f(u)+f(υ) satisfies |e_a-e_b|≤1, here e_a denoting the number of edges labeled a. For the cyclic group Z_k of order K. a Z_k-cordial graph is briefly called a k-cordial graph. It was stated in [1] that odd cycles with leaves attached are k-cordial for all k and that Cycles are k-cordial for all odd k. A cycle on n vertices is simply called an n-cycle. For the k-cordiality of even cycles, Hovey~[1] proposed the following.