Neighborhood alliance in join of a graph with K1

Silvia Leera Sequeira, B. Sooryanarayana, Chandru Hegde

Abstract


Let G = (V,E) be a graph. A subset S of V is called a neighborhood set of G if union of induced subgraph of N[s] is isomorphic to G, where union is taken over all s in S. A defensive alliance is a non-empty subset S of V satisfying the condition that every v ∈ S has at most one more neighbor in V − S than it has in S. The minimum cardinality of any defensive alliance of G is called the alliance number of G. Further, a subset of V which is both a neighborhood set of G as well as a defensive alliance of G is called a neighborhood alliance set, or simply an na-set. The minimum cardinality of an na-set is called neighborhood alliance number of G. The minimum cardinality (in possible cases) of various types of na-sets of join of a graph G with K1, specifically when G is Kn−1, Kn, Cn and Pn are determined in this article.

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Published: 2021-04-05

How to Cite this Article:

Silvia Leera Sequeira, B. Sooryanarayana, Chandru Hegde, Neighborhood alliance in join of a graph with K1, J. Math. Comput. Sci., 11 (2021), 2624-2649

Copyright © 2021 Silvia Leera Sequeira, B. Sooryanarayana, Chandru Hegde. 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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