Total Neighborhood Prime Labeling of Some Graphs

N P Shrimali¹ , Parul B Pandya²

Section:Research Paper, Product Type: Isroset-Journal
Vol.5 , Issue.6 , pp.157-163, Dec-2018

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v5i6.157163

Online published on Dec 31, 2018

Copyright © N P Shrimali, Parul B Pandya . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
Let G=(V,E) be a graph with p vertices and q edges. A bijection f:V(G)∪E(G) → {1,2,3,…,p + q} is said to be total neighborhood prime labeling if it satisfies that, for each vertex of degree at least two, the gcd of labeling on its neighborhood vertices is one and for each vertex of degree at least two, the gcd of labeling on the induced edges is one. In this paper we investigate total neighborhood prime labeling for comb, disjoint union of paths, disjoint union of sunlet graphs, disjoint union of wheel graphs, graph obtained by one copy of path P_n (which has n vertices) and n copies of k_(1,m) and joining i^th vertex of P_n with an edge to fix vertex in the i^th copy of of k_(1,m) , corona product of cycle and star and subdivision of bistar.

Key-Words / Index Term :
Neighborhood prime labeling, Total Neighborhood prime labeling, disjoint union of graphs, corona product of graphs, subdivision of graph

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