Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r ...Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.展开更多
The parameter R（G） is the function about the front three coeffcients of the adjoint polynomial of graph G. In the paper, the range of R（G） is given when β（G） 〈 β（Dn）, where β（G） is the minimum root of th...The parameter R（G） is the function about the front three coeffcients of the adjoint polynomial of graph G. In the paper, the range of R（G） is given when β（G） 〈 β（Dn）, where β（G） is the minimum root of the adjoint polynomial of graph G and the chromatically equivalent classification of tDn is completely depicted.Furthermore, a sufficient and necessary condition for the class of graphs to be chromatically unique is obtained.展开更多
In this paper, we are concerned with the minimum real root of the adjoint polynomial of the connected graph G with cut-vertex u, in which G - u contains paths, circles or Dn components. Here Dn is the graph obtained f...In this paper, we are concerned with the minimum real root of the adjoint polynomial of the connected graph G with cut-vertex u, in which G - u contains paths, circles or Dn components. Here Dn is the graph obtained from K3 and path Pn-2 by identifying a vertex of K3 with an end-vertex of Pn-2. Some relevant ordering relations are obtained. This extends several previous results on the minimum roots of the adjoint polynomials of graphs.展开更多
文摘Let Sn be the star with n vertices, and let G be any connected graph with p vertices. We denote by Eτp＋（r-1）^G（i） the graph obtained from Sr and rG by coinciding the i-th vertex of G with the vertex of degree r - 1 of S,, while the i-th vertex of each component of （r - 1）G be adjacented to r - 1 vertices of degree 1 of St, respectively. By applying the properties of adjoint polynomials, We prove that factorization theorem of adjoint polynomials of kinds of graphs Eτp＋（r-1）^G（i）∪（r - 1）K1 （1 ≤i≤p）. Furthermore, we obtain structure characteristics of chromatically equivalent graphs of their complements.
基金Supported by the National Science Foundation of China(10761008)Supported by the Science Foundation of the State Education Ministry of China(205170)
文摘The parameter R（G） is the function about the front three coeffcients of the adjoint polynomial of graph G. In the paper, the range of R（G） is given when β（G） 〈 β（Dn）, where β（G） is the minimum root of the adjoint polynomial of graph G and the chromatically equivalent classification of tDn is completely depicted.Furthermore, a sufficient and necessary condition for the class of graphs to be chromatically unique is obtained.
基金the National Natural Science Foundation of China (Nos.10461009 10641003)the Key Project of Chinese Ministry of Education (No.206158)
文摘In this paper, we are concerned with the minimum real root of the adjoint polynomial of the connected graph G with cut-vertex u, in which G - u contains paths, circles or Dn components. Here Dn is the graph obtained from K3 and path Pn-2 by identifying a vertex of K3 with an end-vertex of Pn-2. Some relevant ordering relations are obtained. This extends several previous results on the minimum roots of the adjoint polynomials of graphs.
