On the inverse signed total domination number in graphs

Abstract

Abstract.In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on Kr+1-free graphs for r ≥ 2. Also, we bound this parameter for a tree from below in terms of its order and the number of leaves and characterize all trees attaining this bound.

The Generalization of Signed Domination Number of Two Classes of Graphs

“…In recent years, several kinds of signed domination problems in graphs have been investigated [2] [3] [4] [5]. Most of those belong to the vertex domination (or edge domination) of graphs, such as signed (edge) domination [6] [7], minus domination [8], cycle domination [9], signed roman (total) domination [10], weak roman domination [11], inverse signed total domination [12], etc. The signed domination number of cycles n C , paths n P , the square 2 n C of n C and the square 2 n P of n P were given in [13] [14] [15], respectively.…”