Within the effective field theory （EFT）, staggered quadrupolar phase and bicritical point of spin-1 bond and anisotropy dilution Blume-Emery-Griffiths model is studied on simple cubic lattice in the restricted range...Within the effective field theory （EFT）, staggered quadrupolar phase and bicritical point of spin-1 bond and anisotropy dilution Blume-Emery-Griffiths model is studied on simple cubic lattice in the restricted range of biquadratic interaction and bilinear interaction ratio α≤-1. The phase diagrams present a line of staggered quadrupolarparamagnetic （SQ-P） phase and a line of ferromagnetic-paramagnetic （F-P） phase, separated by a bicritical point （BCP）. A large negative ratio and two different dilution factors magnify the range of the SQ phase and reduce range of ferro- magnetic phase in T-α or T-D plane. These parameters can assist the reentrant behavior of the SQ-P line and suppress that of the F-P line. The influence of bond dilution on the BCP is dissimilar to that of anisotropy dilution. There is a degenerate pattern at ground state in T-D plane. Some results obtained by the pure BEG model is in qualitative agreement with the results of Monte Carlo simulations.展开更多
Let G be a simple graph and T={S :S is extreme in G}. If M(V(G), T) is a matroid, then G is called an extreme matroid graph. In this paper, we study the properties of extreme matroid graph.
For a graph G=(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S.The domination numberγ(G)of G is the minimum order of a dominating set in G.A graph G is said to...For a graph G=(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S.The domination numberγ(G)of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,ifγ(G-v)【γ(G)for any vertex v in G.A graph G is domination edge critical,ifγ(G∪e)【γ(G)for any edge e∈/E(G).We call a graph G k-γ-vertex-critical(resp.k-γ-edge-critical)if it is domination vertex critical(resp.domination edge critical)andγ(G)=k.Ananchuen and Plummer posed the conjecture:Let G be a k-connected graph with the minimum degree at least k+1,where k 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is k-factor-critical.In this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph.展开更多
The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings of G.A graph G is PM-compact if the 1-skeleton graph of the prefect matching polytope of G is complete.Eq...The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings of G.A graph G is PM-compact if the 1-skeleton graph of the prefect matching polytope of G is complete.Equivalently,a matchable graph G is PM-compact if and only if for each even cycle C of G,G-V(C)has at most one perfect matching.This paper considers the class of graphs from which deleting any two adjacent vertices or nonadjacent vertices,respectively,the resulting graph has a unique perfect matching.The PM-compact graphs in this class of graphs are presented.展开更多
基金the Key Natural Science Foundation of Education Bureau of Jiangsu Province under Grant No.03KJA140117Jiangsu Thin Film Materials Key Laboratory Open Foundation under Grant No.K2022
文摘Within the effective field theory （EFT）, staggered quadrupolar phase and bicritical point of spin-1 bond and anisotropy dilution Blume-Emery-Griffiths model is studied on simple cubic lattice in the restricted range of biquadratic interaction and bilinear interaction ratio α≤-1. The phase diagrams present a line of staggered quadrupolarparamagnetic （SQ-P） phase and a line of ferromagnetic-paramagnetic （F-P） phase, separated by a bicritical point （BCP）. A large negative ratio and two different dilution factors magnify the range of the SQ phase and reduce range of ferro- magnetic phase in T-α or T-D plane. These parameters can assist the reentrant behavior of the SQ-P line and suppress that of the F-P line. The influence of bond dilution on the BCP is dissimilar to that of anisotropy dilution. There is a degenerate pattern at ground state in T-D plane. Some results obtained by the pure BEG model is in qualitative agreement with the results of Monte Carlo simulations.
文摘Let G be a simple graph and T={S :S is extreme in G}. If M(V(G), T) is a matroid, then G is called an extreme matroid graph. In this paper, we study the properties of extreme matroid graph.
基金supported by Major State Basic Research Development Program of China(973 Project)(Grant No.2006CB805904)Natural Sciences and Engineering Research Council of Canada(Grant No.122059-200)
文摘For a graph G=(V,E),a subset VS is a dominating set if every vertex in V is either in S or is adjacent to a vertex in S.The domination numberγ(G)of G is the minimum order of a dominating set in G.A graph G is said to be domination vertex critical,ifγ(G-v)【γ(G)for any vertex v in G.A graph G is domination edge critical,ifγ(G∪e)【γ(G)for any edge e∈/E(G).We call a graph G k-γ-vertex-critical(resp.k-γ-edge-critical)if it is domination vertex critical(resp.domination edge critical)andγ(G)=k.Ananchuen and Plummer posed the conjecture:Let G be a k-connected graph with the minimum degree at least k+1,where k 2 and k≡|V|(mod 2).If G is 3-γ-edge-critical and claw-free,then G is k-factor-critical.In this paper we present a proof to this conjecture,and we also discuss the properties such as connectivity and bicriticality in 3-γ-vertex-critical claw-free graph.
基金supported by the National Natural Science Foundation of China(Nos.12171440,11971445)。
文摘The perfect matching polytope of a graph G is the convex hull of the incidence vectors of all perfect matchings of G.A graph G is PM-compact if the 1-skeleton graph of the prefect matching polytope of G is complete.Equivalently,a matchable graph G is PM-compact if and only if for each even cycle C of G,G-V(C)has at most one perfect matching.This paper considers the class of graphs from which deleting any two adjacent vertices or nonadjacent vertices,respectively,the resulting graph has a unique perfect matching.The PM-compact graphs in this class of graphs are presented.
