The smallest integer k needed for the assignment of k colors to the elements so that the
coloring is proper (vertices and edges) is called the total chromatic number of a graph …

A molecular network can be characterized by several different ways, like a matrix, a
polynomial, a drawing or a topological descriptor. A topological descriptor is a numeric …

The notion of Roman {2}-domination was introduced in 2016 as a variant of Roman
domination, a concept inspired by a defending strategy used by the emperor Constantine …

The purpose of this survey is to bring some order into the growing literature on a type of
graphs which emerged in the past couple of decades under a wealth of names and in …

In this paper, we obtain the Italian domination number, perfect Italian domination number
and double Roman domination number of generalized Sierpiński graph S (G, 2), where G is …

A total coloring of a graph is an assignment of colors to all the elements of the graph in such
a way that no two adjacent or incident elements receive the same color. In this paper, we …

Abstract The General Randić index R α of a simple graph G is defined as R α (G)=∑ vi∼ vjd
(vi) d (vj) α, where d (vi) denotes the degree of the vertex v i. Rodríguez-Velázquez and …

An Italian dominating function (IDF) of a graph G is a function f: V (G)→{0, 1, 2} satisfying the
condition that for every v∈ V with f (v)= 0,∑ u∈ N (v) f (u)≥ 2. The weight of an IDF on G is …

Shannon entropy, also known as information entropy or entropy, measures the uncertainty
or randomness of probability distribution. Entropy is measured in bits, quantifying the …

A map $ f: V\rightarrow\{0, 1, 2\} $ is a Roman dominating function on a graph $ G=(V, E) $ if
for every vertex $ v\in V $ with $ f (v)= 0$, there exists a vertex $ u $, adjacent to $ v $, such …