also introduce the notion of H-supermagic dual of a H-suermagic labeling and H-supermagic strength of graphs admitting H-supermagic labeling. We construct a chain of any 2-connected graph H, garland mechanical engineering honors thesis graph and linear garland of a 2-connected graph H and prove they are H-supermagic. And is said to be H-supermagic if the vertices of G receive the smaller labels 1, 2, â,p.
Also we prove that the edge amalgamation of a finite number of graphs isomorphic to a given 2-connected graph H, and the one point union of a finite number of copies of a 2-connected graphs are H-supermagic. We establish the relation between H-supermagic labeling and its dual. In this thesis we investigate some graphs that admit cycle-coverings, construct some H-supermagic graphs from a given graph.
We investigate the generalised prism Cm Pn, m 4, the ladder graph P2 Pn, the grid P3 Pn, the generalised antiprism, the triangular ladder Ln, the Fan Graph Fn and k-polygonal snake and proved they are cycle-supermagic. As a special case we find the bounds for the Ph-supermagic strength of path graphs. Home Thesis Abstracts Selvagopal, p Selvagopal mathematics, Manonmaniam Sundaranar University, Tirunelveli, october, 2009. Also we find the H-supermagic strength of some graphs. Ijmsc has been indexed in several world class data bases like Google Scholar, drji (Directory of Research Journals Indexing),Cite Factor, Research Bible. Creative Commons.0 International License. A graph G (V, E) that admits an H-covering is called H â magic if there exists a total labeling such that for all subgraphs of G isomorphic to H, we have, the sum of vertex labeling and edge labeling are the same. If every Hi is isomorphic to a given graph H, then we say that G admits an H â covering.
An edge-covering of a graph G is a family of different subgraphs H1, H2, H3, â, Hk of G such that every edge of E belongs to at least one of the subgraphs Hi for 1. A total labeling f is said to be magic if for all edges xy, f(x)f(y)f(xy) are the same. Abstract, a total labeling is a function from the set of vertices union the set of edges of a (p,q) graph G to the set of natural numbers 1,2,â,. Submitted in partial fulfillment of the requirements for the Bachel or of Science with Distinction in Mathematics.
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