Indian Journal of Science and Technology
Year: 2017, Volume: 10, Issue: 26, Pages: 1-10
Rajakishore Samal1 * and Debdas Mishra2
1Department of Mathematics, O.P.S.Mohavidyalaya, Hindol Road, Dhenkanal – 759019, Odisha, India; [email protected] 2Department of Mathematics, C.V.Raman College of Engineering and Technology, Bhubaneswar – 752054, Odisha, India; [email protected]
*Author for correspondence
Department of Mathematics, O.P.S.Mohavidyalaya, Hindol Road, Dhenkanal – 759019, Odisha, India; [email protected]
Objectives: To explore and identify some new classes of graphs which exhibit polygonal sum labeling. Methods: In this article we use a methodology which fundamentally involves formulation and subsequent mathematical validation. Findings: Here we establish that the graphs – Star ( K1,n ), Coconut Tree, Bistar ( m n, S ), the Graph , , , mnk S Comb ( P K n 1 ) and Subdivision graph S K( 1,n ) admit pentagonal, hexagonal, heptagonal, octagonal, nonagonal and decagonal sum labeling. Applications: One can explore to generalize these results and extend to give n-gonal labeling to some classes graphs. Sum labeling has already been used in the problems involving relational database management and hence one can try out to use polygonal sum labeling as well in these problems.
Keywords: Bistar, Coconut Tree, Comb, Polygonal Sum Labeling, Star, Subdivision Graph
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