Super Magic and Antimagic Labelings of Disjoint Union of Plane Graphs
نویسندگان
چکیده
SUPER MAGIC AND ANTIMAGIC LABELINGS OF DISJOINT UNION OF PLANE GRAPHS Ali Ahmad, Martin Bača, Marcela Lascsáková, Andrea Semaničová-Feňovčíková 2,3 College of computer and information system, Jazan University, Jazan, Saudi Arabia Department of Appl. Mathematics and Informatics, Technical University, Košice, Slovak Republic Abdus Salam School of Mathematical Sciences, G. C. University, Lahore, Pakistan [email protected], [email protected], [email protected], [email protected] ABSTRACT: Suppose G is a finite plane graph with vertex set V(G) and edge set E(G). A d-antimagic labeling of type (1,1,0) of G is a one-to-one map from V(G)E(G) onto the integers 1,2,...,|V(G)|+|E(G)| with the property that the labels of the vertices and edges surrounding the face add up to a weight of that face and the weights of all s-sided faces form an arithmetic progression of difference d. A d-antimagic labeling is called super if the smallest possible labels appear on the vertices. In this paper, we investigate the existence of super d-antimagic labelings of type (1,1,0) for disjoint union of plane graphs for several values of difference d. The work was supported by Higher Education Commission Pakistan Grant HEC(FD)/2007/555 and by Slovak VEGA Grant 1/0130/12.
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