The 1-open neighborhood edge coloring number of a graph
E. Sampathkumar, L. Pushpalatha, Charles Dominic, R. C. Vasundhara · 2011
This paper proposes a new definition, `the 1-open neighborhood edge coloring number of a graph', which shows important progress in the field of graph coloring. The 1-open neighborhood edge coloring number χ′1n(G) of a graph G is the maximum number of colors permitted to color the edges of G such that for each edge e of G, at most one edge adjacent to e receives a color different from that of e. In this paper, the authors obtain some exact values of this parameter for some known graphs, such as paths, cycles, wheels, the Petersen graph, etc., and characterize graphs G for which χ′1n(G)=1. Furthermore, for a graph G with p vertices and q edges with maximum degree Δ, they obtain that χ′1n(G)≤q−Δ+2 and χ′1n(G)≤β+1, where β is the maximum number of independent vertices of degree 2