Every branch of mathematics employs some notion of a product that enables the com-
bination or decomposition of its elemental structures. In graph theory there are four main …

Graph theory experienced a tremendous growth in the 20th century. One of the main
reasons for this phenomenon is the applicability of graph theory in other disciplines such as …

Vizing's conjecture from 1968 asserts that the domination number of the Cartesian product of
two graphs is at least as large as the product of their domination numbers. In this paper we …

We introduce a new setting for dealing with the problem of the domination number of the
Cartesian product of graphs related to Vizing's conjecture. The new framework unifies two …

Vizing conjectured in 1963 that the domination number of the Cartesian product of two
graphs is at least the product of their domination numbers; this remains one of the biggest …

In this paper we introduce the concept of fair reception of a graph which is related to its
domination number. We prove that all graphs G with a fair reception of size γ (G) satisfy …

In 1968, Vizing gave a conjecture: γ (G□ H)≥ γ (G) γ (H) γ(G\,\,\square\,\,H)≥γ(G)γ(H) for
any graphs GG and HH, which is now still open. In the text book “Domination in Graph …

A long-standing Vizing's conjecture asserts that the domination number of the Cartesian
product of two graphs is at least as large as the product of their domination numbers; one of …

The domination polynomials of binary graph operations, aside from union, join and corona,
have not been widely studied. We compute and prove recurrence formulae and properties of …

Let γ (G) be the domination number of a simple graph G and G□ H be the Cartesian product
of two simple graphs G and H. A function f: V (G)→{0, 1, 2} is a Roman dominating function …