应用数学学报
應用數學學報
응용수학학보
ACTA MATHEMATICAE APPLICATAE SINICA
2010年
1期
78-87
,共10页
q-树的二次整子图%二色子图%n阶加点q-树
q-樹的二次整子圖%二色子圖%n階加點q-樹
q-수적이차정자도%이색자도%n계가점q-수
two-degree integral subgraph of q-tree%two-color subgraph%added-vertex q-tree on n vertices
在这篇文章中我们成功地仅用色多项式表征了最小度不等于q-3的q-树的二次整子图和n阶加点q-树,即当图的最小度δ(G)≠q-3时,n阶图G具有色多项式P(G;λ)=λ(λ-1)…(λ-q+2)(λ-q+1)~3(λ-q)~(n-q-2), n≥q+2,当且仅当G是n阶q-树的二次整子图或n阶加点q-树.
在這篇文章中我們成功地僅用色多項式錶徵瞭最小度不等于q-3的q-樹的二次整子圖和n階加點q-樹,即噹圖的最小度δ(G)≠q-3時,n階圖G具有色多項式P(G;λ)=λ(λ-1)…(λ-q+2)(λ-q+1)~3(λ-q)~(n-q-2), n≥q+2,噹且僅噹G是n階q-樹的二次整子圖或n階加點q-樹.
재저편문장중아문성공지부용색다항식표정료최소도불등우q-3적q-수적이차정자도화n계가점q-수,즉당도적최소도δ(G)≠q-3시,n계도G구유색다항식P(G;λ)=λ(λ-1)…(λ-q+2)(λ-q+1)~3(λ-q)~(n-q-2), n≥q+2,당차부당G시n계q-수적이차정자도혹n계가점q-수.
In this paper we have successfully characterized two-degree integral subgraph of q-tree and added-vertex q-tree on n vertices by chromatic polynomials only that if the minimum degree of graph G does not equal q - 3(δ(G) ≠ q - 3), then the graphs with the chromatic polynomial as following P(G;λ)=λ(λ-1)…(λ-q+2)(λ-q+1)~3(λ-q)~(n-q-2), n≥q+2,could only be two-degree integral subgraph of q-tree or added-vertex q-tree on n vertices.
