# Antidegree equitable sets in a graph

Adiga, Chandrashekar and Subba Krishna, K. N. (2015) Antidegree equitable sets in a graph. International Journal of Mathematical Combinatorics, 1. pp. 24-34.

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## Abstract

Let G = (V,E) be a graph. A subset S of V is called a Smarandachely antidegree equitable k-set for any integer k, 0 . k . (G), if |deg(u) . deg(v)| 6= k, for all u, v ?Â¸ S. A Smarandachely antidegree equitable 1-set is usually called an antidegree equitable set. The antidegree equitable number ADe(G), the lower antidegree equitable number ade(G), the independent antidegree equitablenumber ADie(G) and lower independent antidegree equitable number adie(G) are defined as follows: ADe(G) = max|S| : S is a maximal antidegree equitable set in G, ade(G) = min|S| : S is a maximal antidegree equitable set in G, ADie(G) = max|S| : S is a maximal independent and antidegree equitable set in G, adie(G) = min|S| : S is a maximal independent and antidegree equitable set in G. In this paper, we study these four parameters on Smarandachely antidegree equitable 1-sets.

Item Type: Article Smarandachely Antidegree Equitable K-Set and Antidegree Equitable Set and Antide-Gree Equitable Number and Lower Antidegree Equitable Number and Independent Antidegree Equitable Number and Lower Independent Antidegree Equitable Number E Mathematical Science > Mathematics Department of > Mathematics Users 19 not found. 10 Jul 2019 05:16 08 Jul 2022 10:08 http://eprints.uni-mysore.ac.in/id/eprint/5029

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