On the inverse signed total domination number in graphs

In this paper, we study the inverse signed total domination number in graphs and present new lower and upper bounds on this parameter. For example by making use of the classic theorem of Turan (1941), we present a sharp upper bound for graphs with no induced complete subgraph of order greater than two. Also, we bound this parameter for a tree in terms of its order and the number of leaves and characterize all trees attaining this bound

New bounds on the signed total domination number of graphs

In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turan, we present a sharp lower bound on this parameter for graphs with no complete graph of order r+1 as a subgraph. Also, we prove that n-2(s-s') is an upper bound on the signed total domination number of any tree of order n with s support vertices and s' support vertives of degree two. Moreover, we characterize all trees attainig this bound.Comment: This paper contains 11 pages and one figur

On the Signed 22-independence Number of Graphs

In this paper, we study the signed 2-independence number in graphs and give new sharp upper and lower bounds on the signed 2-independence number of a graph by a simple uniform approach. In this way, we can improve and generalize some known results in this area

Bounds on the signed distance--domination number of graphs

Abstract Let , be a graph with vertex set of order and edge set . A -dominating set of is a subset such that each vertex in \ has at least neighbors in . If is a vertex of a graph , the open -neighborhood of , denoted by , is the set , . is the closed -neighborhood of . A function 1, 1 is a signed distance--dominating function of , if for every vertex , ∑ 1. The signed distance--domination number, denoted by , , is the minimum weight of a signed distance--dominating function of . In this paper, we give lower and upper bounds on , of graphs. Also, we determine the signed distance--domination number of graph , (the graph obtained from the disjoint union by adding the edges , ) when 2

Strong geodomination in graphs

A pair x, y of vertices in a nontrivial connected graph G is said to geodominate a vertex v of G if either v ∈ {x, y} or v lies in an x - y geodesic of G. A set S of vertices of G is a geodominating set if every vertex of G is geodominated by some pair of vertices of S. In this paper we study strong geodomination in a graph G