International Journal of Advanced Research and Publications (2456-9992)

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Enumerating Of Star-Magic Coverings And Critical Sets

Volume 4 - Issue 5, May 2020 Edition

Author(s)
Anisatul Farida, Ratna Puspita Indah
Keywords
, critical sets, complete bipartite graph
Abstract
A simple graph admits a H-magic covering if every edge in G belongs to a subgraph of G that isomorphic to H. Let be a complete bipartite graph on m and n vertices. Then graph G is a if there is a total labeling such that for each subgraph of G isomorphic to , there exists , where m(f) is a positif integer called magic sum. When f(V)= we say that G is and we donete its supermagic-sum by s(f). The aim of this research is to list all possible H-magic covering on complete bipartite graph, where H is star magic, especially for n=3. After we list all possible star magic covering on complete biparite graph, we tke s one example of the labeling to find the critical sets. The method f this research is a literary study and we carried outthe enumertion of all possible existing labeling. This research get a sum of 836 labeling which are not isomorphic. After we get list of all possible labeling, we choose a set of label vertices {1,3,4,5,7,10} from which we establish some 28 critical set, 21 of them are of size 1 and the others are of size 2
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