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A NOTE ON DOMSATURATION NUMBER AND DOMSATURATION POLYNOMIAL OF A GRAPH

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W. Jinesha1,∗ , D. Nidha2
» doi: 10.48047/ecb/2023.12.7.339

Abstract

Let ???? be a simple graph of order ????. The domsaturation polynomial of a graph ???? of order ???? is the polynomial ????????(????, ????) = ∑ ????(????, ????) ???? ????=???????? ???? ???? , where ????(????, ????) is the number of dominating sets of ???? of size ????. The domsaturation number of ???? is the least positive integer ???? such that every vertex of ???? lies in a dominating set of cardinality ????. In this paper, we obtain the domination polynomial and minimal domination polynomial of a graph

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