%0 Journal Article
%T NK-Labeling of Graphs
%A Nasreen Almohanna
%A Khawlah Alhulwah
%J American Journal of Computational Mathematics
%P 391-400
%@ 2161-1211
%D 2024
%I Scientific Research Publishing
%R 10.4236/ajcm.2024.144020
%X A graph labeling is the assigning of labels to the vertices, edges, or both (usually non-negative integers), often satisfying some prescribed requirements. This terminology has become standard. A graph G's edges can be colored by assigning a different color to each of its edges. The edge coloring is appropriate if adjacent edges are given different colors. In this work, we introduce a new labeling called NK-labeling. Let
be a proper edge coloring of G which induces a proper vertex coloring
defined by
Such that
is the set of edges incident with
in G. The minimum positive integer for which the graph G has NK-labeling called NK-chromatic index and denoted by
. We study the NK-labeling of several well-known classes of graphs. It is shown that the NK-chromatic of the path
for
is three and for odd