一类稀疏图的邻和可区别边色数
Neighbor sum distinguishing index of a kind of sparse graphs

摘要： 设φ为图G的正常k-边染色。 对任意v∈V(G),令fφ(v)=∑uv∈E(G)φ(uv)。 若对每条边uv∈E(G)都有fφ(u)≠fφ(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。
Abstract: Let φ be a proper k-edge coloring of G. For each vertex v∈V(G), set fφ(v)=∑uv∈E(G)φ(uv). φ is called a k-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, Δ≥6 and mad(G)≤5/2, then χ'Σ(G)=Δ if and only if G has no adjacent vertices of maximum degree