Equitable eccentric domination in graphs

A Riyaz Ur Rehman, A Mohamed Ismayil

Abstract


In this paper, we define equitable eccentric domination in graphs. An eccentric dominating set S ⊆ V (G) of a graph G(V, E) is called an equitable eccentric dominating set if for every v ∈ V − S there exist at least one vertex u ∈ V such that |d(v) − d(u)| ≤ 1 where vu ∈ E(G). We find equitable eccentric domination number γeqed(G) for most popular known graphs. Theorems related to γeqed(G) have been stated and proved.

Keywords


Eccentricity, equitable domination number, equitable eccentric domination number.

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References


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DOI: http://dx.doi.org/10.23755/rm.v47i0.802

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Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.