E^(D(i))形图簇的伴随多项式的因式分解及色性分析

The Factorization of Adjoint Polynomials of Graphs of E~ D(i) -shape with Chromatically Equivalence Analysis

令 Dm表示三阶完全圈 K3 的一个顶点与路 Pm -2 的一个 1度点重迭后得到的图 ;ψ( i)D (k,m)表示把 Dm的第 i个顶点 (第 1个顶点是 1度点 )与星图 Sk+1 的 k度点重迭后得到的图 ;ED ( i)rm+r-1 表示把 r Dm 中一个分支的第 i个顶点与 Sr的 r- 1度点重迭 ,同时把其余 r- 1个分支的第 i个顶点分别与 Sr的 r- 1个 1度点都依次连一条边后得到的图 .我们证明了对于 1≤ i≤ m,r≥ 2 ,图簇ED ( i)rm+r-1 ∪ (r- 1 ) K1 与 Dm ∪ (r- 2 )ψ( i)D (1 ,m)∪ψ( i)D (r,m)两者的补图是色等价的 .

Let D m be the graph consisting of K 3 and the path P m-2 by coinciding a vertex of K 3 with a vertex of degree 1 of P m-2 ; and let ψ (i) D(k,m) denote the graph consisting of D m and the star S k+1 by coinciding ith vertex (First vertex be degree 1) of D m with the vertex of degree k of S k+1 ; and let E D(i) r(m+1)-1 denote the graph obtained from rD m and S r by coinciding the ith vertex of D m with the vertex of degree r-1 of S r, while by adjacenting the ith vertex of everyone of (r-1)D m with r-1 vertices of degree 1 of S r. We prove the complements of two graphs both E D(i) r(m+1)-1 ∪(r-1)K 1 and D m∪(r-1)ψ (i) D(1,m)∪ψ (i) D(r,m) that be chromatically equivalent.