A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H...A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H_(1) and H2.The collection of all least common multiples of H_(1) and H2 is denoted by LCM(H_(1),H_(2))and the size of a least common multiple of H_(1) and H2 is denoted by lcm(H_(1),H_(2)).In this paper lcm(P_(4),□P_(m) P_(n)),lcm(P_(4),C_(m) □C_(n))and lcm(K_(1,3),K_(1,m)□ K_(1,n))aredetermined.展开更多
文摘A graph G without isolated vertices is a least common multiple of two graphs H_(1) and H2 if G is a smallest graph,in terms of number of edges,such that there exists a decomposition of G into edge disjoint copies of H_(1) and H2.The collection of all least common multiples of H_(1) and H2 is denoted by LCM(H_(1),H_(2))and the size of a least common multiple of H_(1) and H2 is denoted by lcm(H_(1),H_(2)).In this paper lcm(P_(4),□P_(m) P_(n)),lcm(P_(4),C_(m) □C_(n))and lcm(K_(1,3),K_(1,m)□ K_(1,n))aredetermined.
