PARTIAL DOMINATION IN THE JOIN, CORONA, LEXICOGRAPHIC AND CARTESIAN PRODUCTS OF GRAPHS

Let G = (V(G), E(G)) be a simple graph and let alpha is an element of (0, 1]. A set S subset of V(G) is an alpha-partial dominating set in G if vertical bar N[S]vertical bar >= alpha vertical bar V(G)vertical bar. The smallest cardinality of an alpha-partial dominating set in G is called the alpha-partial domination number of G, denoted by partial derivative(alpha)(G). This paper extends the study on partial domination in graphs independently worked on by Case et al. [5] and Das [7] who published papers of the same title in May 2017 and July 2017, respectively. It also introduces the concept of total partial domination. In this paper, we characterize the partial dominating sets in the join, corona, lexicographic and Cartesian products of graphs and determine the exact values or sharp bounds of the corresponding partial domination number of these graphs.