An H-covering(resp.decomposition) of a graph G is a set of subgraphs of G,{H1,H2,…,Hk} such that H1 is isomorphic to H for eachi,and each edge of G belongs to at least(resp.exactly) one of the subgraphs Hi,fox 1≤i≤...An H-covering(resp.decomposition) of a graph G is a set of subgraphs of G,{H1,H2,…,Hk} such that H1 is isomorphic to H for eachi,and each edge of G belongs to at least(resp.exactly) one of the subgraphs Hi,fox 1≤i≤k.An H-covering(resp.decomposition) of a graph G is a magic H-covering(resp.decomposition) if there is a bijection f:V(G)∪E(G)→{1,...,|V(G)|+|E(G)|} such that the sum of labels of edges and the vertices of each copy of H in the decomposition is a constant.If G admits a unique H-covering H and H is a magic H-covering of G,then G is H-magic.In this paper,we show that if G admits a magic H-covering(resp.decomposition),and satisfies some other conditions,then a union of k vertex joint graph G,kG,and a graph obtained from kG,Gk admit a magic H-covering or decomposition.展开更多
基金Supported by the National Natural Science Foundation of China(11702094)the Fundamental Research Funds for the Central Universities(3142015043)North China Institute of Science and Technology Applied Mathematics Innovation Team(3142018059)。
文摘An H-covering(resp.decomposition) of a graph G is a set of subgraphs of G,{H1,H2,…,Hk} such that H1 is isomorphic to H for eachi,and each edge of G belongs to at least(resp.exactly) one of the subgraphs Hi,fox 1≤i≤k.An H-covering(resp.decomposition) of a graph G is a magic H-covering(resp.decomposition) if there is a bijection f:V(G)∪E(G)→{1,...,|V(G)|+|E(G)|} such that the sum of labels of edges and the vertices of each copy of H in the decomposition is a constant.If G admits a unique H-covering H and H is a magic H-covering of G,then G is H-magic.In this paper,we show that if G admits a magic H-covering(resp.decomposition),and satisfies some other conditions,then a union of k vertex joint graph G,kG,and a graph obtained from kG,Gk admit a magic H-covering or decomposition.
