摘要
设φ为图G的正常k-边染色。对任意v∈V(G),令f_φ(v)=Σuv∈E(G)φ(uv)。若对每条边uv∈E(G)都有f_φ(u)≠f_φ(v),则称φ为图G的k-邻和可区别边染色。图G存在k-邻和可区别边染色的k的最小值称为G的邻和可区别边色数,记作χ'_Σ(G)。确定了一类稀疏图的邻和可区别边色数,得到:若图G不含孤立边,Δ≥6且mad(G)≤5/2,则χ'_Σ(G)=Δ当且仅当G不含相邻最大度点。
Let φ be a proper k-edge coloring of G. For each vertex v∈V（G）,set fφ（v）=Σuv∈E（G）φ（uv） ,φ is called ak-neighbor sum distinguishing edge coloring of G if fφ（u）≠fφ（v）for each edge uv E（G）. The smallest k such that G has a k-neighbor sum distinguishing edge coloring is called the neighbor sum distinguishing index, denoted by χ＇Σ（G）The neighbor sum distinguishing index of a kind of sparse graphs is determined. It is proved that if G is a graph without isolated edges, △≥ 6 and mad （G）≤5/2,then χ＇_Σ（G）=Δif and only if G has no adjacent vertices ofmaximum degree.
出处
《山东大学学报（理学版）》
CAS
CSCD
北大核心
2017年第8期94-99,共6页
Journal of Shandong University(Natural Science)
基金
国家自然科学基金资助项目(11671232
11301134
11301135)
河北省自然科学基金资助项目(A2015202301)
河北省高等学校科学技术研究重点项目(ZD2015106)
关键词
邻和可区别边染色
最大平均度
稀疏图
neighbor sum distinguishing edge coloring
maximum average degree
sparse graph
