Further Results on Dual Domination in Graphs
V.Lavanya1, D. S. T. Ramesh2, N.Meena3
1V.Lavanya*, Research Scholar, Department of Mathematics, Nazareth Margoschis College, Pillaiyanmanai,Thoothukudi, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, TamilNadu, India.
2D.S.T.Ramesh, Department of Mathematics, Nazareth Margoschis College, Pillaiyanmanai,Thoothukudi, Affiliated to Manonmaniainm Sundaranar University, Abishekapatti, Tirunelveli, TamilNadu, India.
3N.Meena, Department of Mathematics, The M.D.T Hindu College, Pettai, Tirunelveli, Affiliated to Manonmaniam Sundaranar University, Abishekapatti, Tirunelveli, TamilNadu, India.
Manuscript received on May 06, 2020. | Revised Manuscript received on May 15, 2020. | Manuscript published on June 30, 2020. | PP: 1949-1954 | Volume-9 Issue-5, June 2020. | Retrieval Number: C5588029320/2020©BEIESP | DOI: 10.35940/ijeat.C5588.029320
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© The Authors. Blue Eyes Intelligence Engineering and Sciences Publication (BEIESP). This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)
Abstract: Let G = (V, E) be a simple graph. A set S V(G) is a dual dominating set of G (or bi-dominating set of G) if S is a dominating set of G and every vertex in S dominates exactly two vertices in V-S. The dual-domination number γdu(G) (or bi-domination number (G) bi ) of a graph G is the minimum cardinality of the minimal dual dominating set (or dual dominating set). In this paper dual domination number and relation with other graph parameters are determined.
Keywords: Domination, dual-domination, chromatic number and connectivity.