This chapter is concerned with the concept Roman domination in graphs, which was
introduced in 2004 by Cockayne, Dreyer, SM Hedetniemi, and ST Hedetniemi based on the …

For a given graph G, the well-known Randić index of G, introduced by Milan Randić in 1975,
is defined as R (G)=∑ uv∈ E (G)(dudv)− 1/2, where the sum is taken over all edges uv and …

The discharging method is most well-known for its central role in the proof of the Four Color
Theorem. This proof technique was extensively applied to study various graph coloring …

Let γ r 2 (G) be the 2-rainbow domination number of a graph G. In our work, we solve an
open question for 2-rainbow domination number of general Petersen graphs P (n, k). In …

Let γ i (Cm⎕ Cn) denote the independent domination number of the strong product of the
graphs Cm, the cycle of length m, m≥ 3 and the graph Cn, the cycle of length n, n≥ 3. In this …

Graph distance measures based on topological indices have been already explored by
Dehmer et al. Also, inequalities for those graph distance measures have been proved. In this …

Let G be a simple graph with order n and µ1, µ2,..., µn be the roots of its matching
polynomial. The matching energy of G is defined to be the sum of the absolute values of µi …

Given a positive integer t and a graph F, the goal is to assign a subset of the color set {1, 2,
..., t\} 1, 2,…, t to every vertex of F such that every vertex with the empty set assigned has all t …

In this paper, we study the most basic domination invariants in graphs, in which number 2 is
intrinsic part of their definitions. We classify them upon three criteria, two of which give the …

Let k≥ 1 be an integer, and let G be a graph. A k-rainbow dominating function (or a k-RDF)
of G is a function f from the vertex set V (G) to the family of all subsets of {1, 2,..., k} such that …