a function $f:v(g)rightarrow {-1,0,1}$ is a {em minusdominating function} if for every vertex $vin v(g)$, $sum_{uinn[v]}f(u)ge 1$. a minus dominating function $f$ of $g$ is calleda {em global minus dominating function} if $f$ is also a minusdominating function of the complement $overline{g}$ of $g$. the{em global minus domination number} $gamma_{g}^-(g)$ of $g$ isdefined as $gamma_{g}^-(g)=min{...

4 In this paper, we study the domination number, the global dom5 ination number, the cographic domination number, the global co6 graphic domination number and the independent domination number 7 of all the graph products which are non-complete extended p-sums 8 (NEPS) of two graphs. 9

In this paper, we present new upper bounds for the global domination and Roman domination numbers and also prove that these results are asymptotically best possible. Moreover, we give upper bounds for the restrained domination and total restrained domination numbers for large classes of graphs, and show that, for almost all graphs, the restrained domination number is equal to the domination num...

A function f : V (G) → {−1, 0, 1} is a minus dominating function if for every vertex v ∈ V (G), ∑ u∈N [v] f(u) ≥ 1. A minus dominating function f of G is called a global minus dominating function if f is also a minus dominating function of the complement G of G. The global minus domination number γ− g (G) of G is defined as γ − g (G) = min{ ∑ v∈V (G) f(v) | f is a global minus dominating functi...

A set S ⊆ V is a global dominating set of a graph G = (V,E) if S is a dominating set of G and G, where G is the complement graph of G. The global domination number γg(G) equals the minimum cardinality of a global dominating set of G. The square graph G of a graph G is the graph with vertex set V and two vertices are adjacent in G if they are joined in G by a path of length one or two. In this p...

Domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This thesis focuses on domination theory, and the main aim of the study is to apply a probabilistic approach to obtain new upper bounds for various domination parameters. Chapters 2 and ...

A dominating set S of a graph G is called locating-dominating, LD-set for short, if every vertex v not in S is uniquely determined by the set of neighbors of v belonging to S. Locating-dominating sets of minimum cardinality are called LD-codes and the cardinality of an LD-code is the location-domination number λ(G). An LD-set S of a graph G is global if it is an LD-set of both G and its complem...

A subset S of vertices in a graph G is a global total dominating set, or just GTDS, if S is a total dominating set of both G and G. The global total domination number γgt(G) of G is the minimum cardinality of a GTDS of G. We present bounds for the global total domination number in graphs.

In this paper we compute for paths and cycles certain graph domination invariants like locating domination number, differentiating domination number, global alliance number etc., We also do some comparison analysis of certain parameters defined by combining the domination measures and the second smallest eigen value of the Laplacian matrix of all connected graphs of order 4.While discussing app...