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On edge product cordial graphs

Ivanco Jaroslav

Opuscula Mathematica

2019

Vol. 39, no. 5

691--703

An edge product cordial labeling is a variant of the well-known cordial labeling. In this paper we characterize graphs admitting an edge product cordial labeling. Using this characterization we investigate the edge product cordiality of broad classes of graphs, namely, dense graphs, dense bipartite graphs, connected regular graphs, unions of some graphs, direct products of some bipartite graphs, joins of some graphs, maximal k-degenerate and related graphs, product cordial graphs.

M2-edge colorings of dense graphs

Ivanco J.

Opuscula Mathematica

2016

Vol. 36, no. 5

603–-612

An edge coloring φ of a graph G is called an Mi-edge coloring if [formula] every vertex v of G, where φ (v) is the set of colors of edges incident with v. Let K1(G) denote the maximum number of colors used in an Mi-edge coloring of G. In this paper we establish some bounds of K.2(G), present some graphs achieving the bounds and determine exact values of K.2(G) for dense graphs.