A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a...A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a generalized Petersen graph with n=0(mod 5)and k=2,3(mod 5),then E(P(n,k))can be partitioned into five DIMs.Meanwhile,in the left cases k=0,1,4(mod 5),we build some counterexamples to show that there exist some P(n,k)'s which are DIM-free.展开更多
广义Petersen图Pk,n是一种在图论中具有重要研究价值的正则图,其独特的对称性与复杂的结构特性使其在图论中具有广泛的应用价值。文章以广义Petersen图中的P2,7为研究对象,通过深入分析其顶点构造与自同构群的特性,结合严格的理论推导,...广义Petersen图Pk,n是一种在图论中具有重要研究价值的正则图,其独特的对称性与复杂的结构特性使其在图论中具有广泛的应用价值。文章以广义Petersen图中的P2,7为研究对象,通过深入分析其顶点构造与自同构群的特性,结合严格的理论推导,详细证明了P2,7并非边传递图。The generalized Petersen graph Pk,nis a class of regular graphs with significant research value in graph theory. Its unique symmetry and complex structural properties make it widely applicable in various areas of graph theory. This paper focuses on the generalized Petersen graph P2,7, conducting an in-depth analysis of its vertex construction and automorphism group. Through rigorous theoretical derivation, it is demonstrated in detail that P2,7is not edge-transitive, providing new theoretical insights into the study of symmetry and transitivity in generalized Petersen graphs.展开更多
基于Petersen图，提出了Binary Tree Petersen的网络结构，并对其特性进行了研究，证明了Binary Tree Petersen网络具有正则性以及良好的可扩展性，同时还具有比RP（k）、2-DToms更短的直径和良好的并行能力．另外，还基于Binary Tree P...基于Petersen图，提出了Binary Tree Petersen的网络结构，并对其特性进行了研究，证明了Binary Tree Petersen网络具有正则性以及良好的可扩展性，同时还具有比RP（k）、2-DToms更短的直径和良好的并行能力．另外，还基于Binary Tree Petersen网络分别给出了其上的单播和广播路由算法，证明了通信效率都为2j＋4．展开更多
基金Ming Chen was supported by National Key Research and Development Program of China(No.2024YFA1013900)。
文摘A dominating induced matching(DIM)of G is an induced matching that dominates every edge of G.In this note,we completely determine the number of DIMs in the generalized Petersen graph P(n,k).We prove that if P(n,k)is a generalized Petersen graph with n=0(mod 5)and k=2,3(mod 5),then E(P(n,k))can be partitioned into five DIMs.Meanwhile,in the left cases k=0,1,4(mod 5),we build some counterexamples to show that there exist some P(n,k)'s which are DIM-free.
文摘广义Petersen图Pk,n是一种在图论中具有重要研究价值的正则图,其独特的对称性与复杂的结构特性使其在图论中具有广泛的应用价值。文章以广义Petersen图中的P2,7为研究对象,通过深入分析其顶点构造与自同构群的特性,结合严格的理论推导,详细证明了P2,7并非边传递图。The generalized Petersen graph Pk,nis a class of regular graphs with significant research value in graph theory. Its unique symmetry and complex structural properties make it widely applicable in various areas of graph theory. This paper focuses on the generalized Petersen graph P2,7, conducting an in-depth analysis of its vertex construction and automorphism group. Through rigorous theoretical derivation, it is demonstrated in detail that P2,7is not edge-transitive, providing new theoretical insights into the study of symmetry and transitivity in generalized Petersen graphs.
文摘基于Petersen图，提出了Binary Tree Petersen的网络结构，并对其特性进行了研究，证明了Binary Tree Petersen网络具有正则性以及良好的可扩展性，同时还具有比RP（k）、2-DToms更短的直径和良好的并行能力．另外，还基于Binary Tree Petersen网络分别给出了其上的单播和广播路由算法，证明了通信效率都为2j＋4．
基金This work was supported by National Natural Science Foundation of China Grant No.60174049Key Project of Education Department of Hubei Province (2001A43007).
