Minimum clique-clique dominating energy of a graph

Sayinath Udupa, R. S. Bhat, N. Prathviraj

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1 Citation (Scopus)

Abstract

Let C(G) denotes the set of all cliques of a graph G. Two cliques in G are adjacent if there is a vertex incident on them. Two cliques c1, c2 ∈ C(G) are said to clique-clique dominate (cc-dominate) each other if there is a vertex incident with c1 and c2 . A set L ⊆ C(G) is said to be a cc-dominating set (CCD-set) if every clique in G is cc-dominated by some clique in L. The cc-domination number γcc = γcc(G) is the order of a minimum cc-dominating set of G. In this paper we introduce minimum cc-dominating energy of the graph denoting it as Ecc (G). It depends both on underlying graph of G and its particular minimum cc-dominating set (γcc-set) of G. Upper and lower bounds for Ecc (G) are established.

Original languageEnglish
Pages (from-to)3237-3246
Number of pages10
JournalAdvances in Mathematics: Scientific Journal
Volume9
Issue number6
DOIs
Publication statusPublished - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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