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Title: H-Supermagic Labeling of Graphs
Authors: Asif, Muhammad
Keywords: Physical Sciences
Issue Date: 2020
Publisher: Islamia College Peshawar.
Abstract: An edge-covering of a graph G = (V, E, Φ) is a family of distinct sub-graphs H1, H2, . . . , Hk of G such that each edge of E(G) belongs to at least one of the sub-graphs Hi , 1 ≤ i ≤ k. If such phenomena exists then G is said to be admits an (H1, H2, . . . , Hk)-edge covering. If every Hi is isomorphic to a given sub-graph H of G, then in this case G is said to be admit an H-covering. The H-covering is said to be H-decomposition of G if all the sub-graphs in the covering are edge-disjoint. A simple undirected graph G = (V, E, Φ) admits a cycle-covering if every edge in E(G) belongs to at least one sub-graph of G isomorphic to a given cycle C. The graph G is C-magic if there exists a total labeling f : V (G) ∪ E(G) → {1, 2, . . . , |V (G)| + |E(G)|} such that for every subgraph H0 = (V (H0 ), E(H0 )) of G isomorphic to C, the sum P v∈V (H0) f(v) + P e∈E(H0) f(e) is constant. When {f(v) : v ∈ V (G)} = {1, 2, . . . , |V (G)|} then G is said to be C-supermagic. In this thesis, we investigate the cycle-supermagic behavior of disjoint union of graphs, planar graphs and graphs embedded on the surface of torus. We study the cycle-supermagic labeling of a pumpkin graph and two classes of planar maps containing 8-sided and 4-sided faces or 6-sided and 4-sided faces, respectively. Also we study the cyclic super magic labeling for Toroidal and Klein Bottle Fullerenes.
Gov't Doc #: 23183
Appears in Collections:PhD Thesis of All Public / Private Sector Universities / DAIs.

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