NK-Labeling of Graphs  

作　　者：Nasreen Almohanna Khawlah Alhulwah Nasreen Almohanna;Khawlah Alhulwah(Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia)

机构地区：[1]Department of Mathematics and Statistics, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

出　　处：《American Journal of Computational Mathematics》2024年第4期391-400,共10页美国计算数学期刊(英文)

摘　　要：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.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.

关 键 词：Graph Edge Coloring NK-Labeling LABEL Path CYCLE WHEEL Complete Graph 

分 类 号：O15[理学—数学]