On Connected Partial Domination in Graphs
Keywords:Partial domination, Connected Partial domination, Join, Corona, Lexicographic product, Cartesian product
This paper introduces and investigates a variant of partial domination called the connected Î±-partial domination. For any graph G = (V (G), E(G)) and Î± âˆˆ (0, 1], a set S âŠ† V (G) is an Î±-partial dominating set in G if |N[S]| â‰¥ Î± |V (G)|. An Î±-partial dominating set S âŠ† V (G) is a connected Î±-partial dominating set in G if âŸ¨SâŸ©, the subgraph induced by S, is connected. The connected Î±-partial domination number of G, denoted by âˆ‚CÎ±(G), is the smallest cardinality of a connected Î±-partial dominating set in G. In this paper, we characterize the connected Î±-partial dominating sets in the join and lexicographic product of graphs for any Î± âˆˆ (0, 1] and determine the corresponding connected Î±-partial domination numbers of graphs resulting from the said binary operations. Moreover, we establish sharp bounds for the connected Î±-partial domination numbers of the corona and Cartesian product of graphs. Furthermore, we determine âˆ‚CÎ±(G) of some special graphs when Î± =1/2. Several realization problems are also generated in this paper.
How to Cite
Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.
European Journal of Pure and Applied Mathematics will be Copyright Holder.