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H-Magic and H-Supermagic of Graphs

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An H-covering(resp.decomposition) of a graph G is a set of subgraphs of G,{H1,H2,…,Hk } such that Hi is isomorphic to H for each i,and each edge of G belongs to at least (resp.ex actly) one of the subgraphs Hi,for 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)UE(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.IfG 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 ifG admits a magic H-covering (resp.decomposition),and satisfies some other conditions,then a union ofk vertex joint graph G,kG,and a graph obtained from kG,Gk admit a magic H-covering or decomposition.

H-coveringH-decompositionH-magicmagic H-coveringmagic H-decomposition

MIAO Wenjing、WANG Tao、SUI Lili

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Department of Foundation, North China Institute of Science and Technology, Sanhe 065201, Hebei, China

Supported by the National Natural Science Foundation of ChinaFundamental Research Funds for the Central Universitiesand North China Institute of Science and Technology Applied Mathematics Innovation Team

1170209431420150433142018059

2020

武汉大学自然科学学报(英文版)
武汉大学

武汉大学自然科学学报(英文版)

CSTPCDCSCD
影响因子：0.066
ISSN：1007-1202
年,卷(期)：2020.25(2)
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