南昌大学学报（理科版）
南昌大學學報（理科版）
남창대학학보（이과판）
JOURNAL OF NANCHANG UNIVERSITY(NATURAL SCIENCE)
2014年
2期
107-111
,共5页
色多项式%伴随多项式%因式分解%色等价性
色多項式%伴隨多項式%因式分解%色等價性
색다항식%반수다항식%인식분해%색등개성
Chromatic polynomial%Adj oint polynomials%Factorization%Chromatically equivalence
设Pm 和Cm 分别表示具有m个顶点的路和圈，G是任意的r阶连通图，设m是正奇数，把路Pm 的标号为奇数的2-1（m＋1）个顶点分别与2-1（m＋1）G每个分支的第i 个顶点Vi 重迭后所得到的图记为ρG（i）m＋2-1（m＋1）r。运用图的伴随多项式的性质，首先给出了一类图簇ρG（i）（2m＋2）＋（（m＋1）r的伴随多项式。进而令m＝2t-1q-1，λn＝（2nq-1）＋2n-1qr，在讨论上述图的伴随多项式的基础上，我们证明了图ρG（i）λt 和ρG（i）λt ∪（t-1）K1的伴随多项式的因式分解定理，进而证明了这些图类的补图的色等价性。
設Pm 和Cm 分彆錶示具有m箇頂點的路和圈，G是任意的r階連通圖，設m是正奇數，把路Pm 的標號為奇數的2-1（m＋1）箇頂點分彆與2-1（m＋1）G每箇分支的第i 箇頂點Vi 重迭後所得到的圖記為ρG（i）m＋2-1（m＋1）r。運用圖的伴隨多項式的性質，首先給齣瞭一類圖簇ρG（i）（2m＋2）＋（（m＋1）r的伴隨多項式。進而令m＝2t-1q-1，λn＝（2nq-1）＋2n-1qr，在討論上述圖的伴隨多項式的基礎上，我們證明瞭圖ρG（i）λt 和ρG（i）λt ∪（t-1）K1的伴隨多項式的因式分解定理，進而證明瞭這些圖類的補圖的色等價性。
설Pm 화Cm 분별표시구유m개정점적로화권，G시임의적r계련통도，설m시정기수，파로Pm 적표호위기수적2-1（m＋1）개정점분별여2-1（m＋1）G매개분지적제i 개정점Vi 중질후소득도적도기위ρG（i）m＋2-1（m＋1）r。운용도적반수다항식적성질，수선급출료일류도족ρG（i）（2m＋2）＋（（m＋1）r적반수다항식。진이령m＝2t-1q-1，λn＝（2nq-1）＋2n-1qr，재토론상술도적반수다항식적기출상，아문증명료도ρG（i）λt 화ρG（i）λt ∪（t-1）K1적반수다항식적인식분해정리，진이증명료저사도류적보도적색등개성。
It used the symbol Pm to denote a path with n vertices and Cm to denote a cycle with n vertices.In addition,G was a connective graph with r vertices and let be an odd number,then these were denoted byρG(i)m+2-1(m+1)r.The graph consisting of Pm and 2-1(m+1)G by coinciding m vertices were marked“odd”with the vertexVi of every component of Pm and 2-1(m+1)G,respectively.By applying the properties of adjoint polynomials,we gave the adjoint polynomials of a kind of graphsρG(i)(2m+2)+((m+1)r,Let m=2t-1q-1 andλn=(2nq-1 )+2n-1 qr,which was based on the several adj oint polynomials of graphs discussed above.It also proved the factorizations Theorem of adjoint polynomials of graphsρG(i)λt andρG(i)λt ∪(t-1)K1 .Furthermore, the chromatically equivalent graphs of their complements were therefore verified.
