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 c...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 c:E(G)→ℕbe a proper edge coloring of G which induces a proper vertex coloring c′:V(G)→ℤndefined by c′(v)≡∑e∈Evc(e)modnSuch that Evis the set of edges incident with vin G. The minimum positive integer for which the graph G has NK-labeling called NK-chromatic index and denoted by χ′NK(G). We study the NK-labeling of several well-known classes of graphs. It is shown that the NK-chromatic of the path Pnfor n≥4is three and for odd n, the NK-chromatic of the complete graph Knis n. Other results dealing with the NK-labeling are also presented.展开更多
文摘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 c:E(G)→ℕbe a proper edge coloring of G which induces a proper vertex coloring c′:V(G)→ℤndefined by c′(v)≡∑e∈Evc(e)modnSuch that Evis the set of edges incident with vin G. The minimum positive integer for which the graph G has NK-labeling called NK-chromatic index and denoted by χ′NK(G). We study the NK-labeling of several well-known classes of graphs. It is shown that the NK-chromatic of the path Pnfor n≥4is three and for odd n, the NK-chromatic of the complete graph Knis n. Other results dealing with the NK-labeling are also presented.
