A set S of vertices of a graph G is called a decycling set if G-S is acyclic.The smallest size of a decycling set is called the decycling number of G and is denoted by ∇(G).In this paper,we investigate the decycling n...A set S of vertices of a graph G is called a decycling set if G-S is acyclic.The smallest size of a decycling set is called the decycling number of G and is denoted by ∇(G).In this paper,we investigate the decycling number of type-k Halin graphs,focusing on those that are formed from trees that have just two degrees k and 3.For any type-k Halin graph G of order n,we prove that(k-2)n+k^(2)-4k+5/(k-1)^(2)≤∇(G)≤n+k-3/k-1.The result not only supports the largest forest conjecture due to Albertson and Berman(1976),but also offers a tight lower bound for the decycling number of type-3 Halin graphs and several type-k Halin graphs.Moreover,a new formula to determine the cardinality of any decycling set S of a type-k Halin graph G is provided.展开更多
A 3-dimensional type-K competitive Lotka-Volterra system is considered in this paper. Two discretization schemes are applied to the system with an positive interior fixed point, and two corresponding discrete systems ...A 3-dimensional type-K competitive Lotka-Volterra system is considered in this paper. Two discretization schemes are applied to the system with an positive interior fixed point, and two corresponding discrete systems are obtained. By analyzing the local dynamics of the corresponding discrete system near the interior fixed point, it is showed that this system is not dynamically consistent with the continuous counterpart system.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.11171114,11401576)Hotan Prefecture Science and Technology Bureau General Project(Grant No.20220212)。
文摘A set S of vertices of a graph G is called a decycling set if G-S is acyclic.The smallest size of a decycling set is called the decycling number of G and is denoted by ∇(G).In this paper,we investigate the decycling number of type-k Halin graphs,focusing on those that are formed from trees that have just two degrees k and 3.For any type-k Halin graph G of order n,we prove that(k-2)n+k^(2)-4k+5/(k-1)^(2)≤∇(G)≤n+k-3/k-1.The result not only supports the largest forest conjecture due to Albertson and Berman(1976),but also offers a tight lower bound for the decycling number of type-3 Halin graphs and several type-k Halin graphs.Moreover,a new formula to determine the cardinality of any decycling set S of a type-k Halin graph G is provided.
基金Supported by the Natural Science Foundation of Shandong Province (ZR2009AL010)Project of Shandong Province Higher Educational Science and Technology Program (J09LA51)Program for Innovative Research Team in Ludong University (08-CXB005)
文摘A 3-dimensional type-K competitive Lotka-Volterra system is considered in this paper. Two discretization schemes are applied to the system with an positive interior fixed point, and two corresponding discrete systems are obtained. By analyzing the local dynamics of the corresponding discrete system near the interior fixed point, it is showed that this system is not dynamically consistent with the continuous counterpart system.
