TY - JOUR
AU - Cabulao, Jessa Mae Carpentero
AU - Isla, Rowena T.
PY - 2021/11/10
Y2 - 2023/02/02
TI - On Connected Partial Domination in Graphs
JF - European Journal of Pure and Applied Mathematics
JA - Eur. J. Pure Appl. Math.
VL - 14
IS - 4
SE -
DO - 10.29020/nybg.ejpam.v14i4.4168
UR - https://ejpam.com/index.php/ejpam/article/view/4168
SP - 1490-1506
AB - <p>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.</p>
ER -