Double Domination Number of Some Families of Graph
Manjula. C. Gudgeri1, Varsha2
1Dr.Manjula. C. Gudgeri, Professor, KLEMSSCET, Belagavi, India.
2Mrs. Varsha, Research Scholar, KLEMSSCET, Belagavi, India.
Manuscript received on May 25, 2020. | Revised Manuscript received on June 29, 2020. | Manuscript published on July 30, 2020. | PP: 161-164 | Volume-9 Issue-2, July 2020. | Retrieval Number: B3307079220/2020©BEIESP | DOI: 10.35940/ijrte.B3307.079220
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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: In a graph G = (V, E) each vertex is said to dominate every vertex in its closed neighborhood. In a graph G, if S is a subset of V then S is a double dominating set of G if every vertex in V is dominated by at least two vertices in S. The smallest cardinality of a double dominating set is called the double domination number γx2 (G). . In this paper, we computed some relations between double domination number, domination number, number of vertices (n) and maximum degree (Δ) of Helm graph, Friendship graph, Ladder graph, Circular Ladder graph, Barbell graph, Gear graph and Firecracker graph.
Keywords: Dominating set, domination number, double dominating set, double domination number. We denote n, Δ respectively by number of vertices, maximum degree of a graph G.