EXCELLENT-JUST EXCELLENT-DEGREE EQUITABLE DOMINATION IN GRAPHS

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V. Swaminathan, K. D. (2013). EXCELLENT-JUST EXCELLENT-DEGREE EQUITABLE DOMINATION IN GRAPHS. Asian Journal of Current Engineering and Maths, 1(2). Retrieved from https://innovativejournal.in/index.php/ajcem/article/view/35
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Abstract

Let G = (V, E) be a simple graph. A subset D of V(G) is said to be a degree equitable dominating set of G if for every there exists a vertex such that u and v are adjacent &1)vdeg()udeg(≤−. The minimum cardinality of a degree equitable dominating set of G is denoted by )G(eγ. A degree equitable dominating set of G of minimum cardinality is called as a eγ-set of G. G is said to be eγ-excellent if every vertex of G belongs to a eγ-set of G. This paper aims at the study of the new concept namely degree equitable excellent graphs. Just eγ-excellence is also defined and studied. Results on these new concepts are compared with those with respect to domination excellence and justγ-excellence in graphs. 2010 Mathematics Subject Classification : 05C69

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