无限路及其笛卡尔积、直积的孪生α-距离边染色

On Twin α-distance Edge Coloring of Infinite Path and Its Cartesian Product and Direct Product

图G的孪生α-距离边染色是指按模色和能诱导出α-距离点染色的k-α-距离边染色,最小的k值称为α的孪生α-距离边色数,记为ind_(α)^(m),_(α)(G),其中颜色集合为{0,1,…,k-1}.当α=1时,α的孪生1-距离边染色也叫孪生边染色,记为ind_(1)^(m),_(1)(G)或χ_(t)’(G);当α=2时,α的孪生2-距离边染色也叫孪生强边染色,记为ind_(2)^(m),_(2)(G)或χ’_(s,t)(G).文章主要研究无限路的孪生强边染色,以及无限路的笛卡尔积、直积的孪生边染色,并得到了相应的染色数.

κ-α-distance edge colorings of a graph Gthat can induceα-distance vertex coloring of Gby module color sum,which is called twin k-edge coloring ofα-distance with graph G.The minimum κ is called twin edge chromatic number ofα-distance with graph G,defined by ind_(α)^(m),_(α)(G),where the color sets is{0,1,…,k-1}.The edge coloring of graph Gis called twin edge coloring whenα=1,defined by ind_(1)^(m),_(1)(G)or χ_(t)’(G).The edge coloring of graph Gis called twin strong edge coloring whenα=2,defined by ind_(2)^(m),_(2)orχ’_(s,t)(G).In this paper,we studied that twin strong edge coloring of infinite path,twin edge coloring of the Cartesian product and direct product of infinite path,and it’s edge chromatic number which was obtained.