Browsing by Subject "strong product"

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Access status: Open Access ,
On the existence of independent (1,k) -dominating sets for k∈{1,2} in two products of graphs
(Wydawnictwa AGH, 2026) Bednarz, Paweł; Michalski, Adrian; Paja, Natalia
A subset $J$ of vertices is said to be a $(1,k)$-dominating set if every vertex $v$ not belonging to the set $J$ has a neighbour in $J$ and there exists also another vertex in $J$ within the distance at most $k$ from $v$. In this paper, we study the problem of the existence of independent $(1,k)$-dominating sets for $k\in\{1,2\}$ in the tensor product and in the strong product of two graphs. We give complete characterisations of these graph products, which have independent $(1,1)$-dominating sets or independent $(1,2)$-dominating sets, with respect to the properties of their factors.
Access status: Open Access ,
Wiener index of strong product of graphs
(Wydawnictwa AGH, 2018) Peterin, Iztok; Žigert Pleteršek, Petra
The Wiener index of a connected graph $G$ is the sum of distances between all pairs of vertices of $G$. The strong product is one of the four most investigated graph products. In this paper the general formula for the Wiener index of the strong product of connected graphs is given. The formula can be simplified if both factors are graphs with the constant eccentricity. Consequently, closed formulas for the Wiener index of the strong product of a connected graph $G$ of constant eccentricity with a cycle are derived.