Simon Brezovnik

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math.CO2026

Upper bounds for double Roman domination and $[k]$ -Roman domination of cylindrical graphs $C_{m} □ P_{n}$

Simon Brezovnik, Janez Žerovnik

Roman-type domination parameters form an important class of graph invariants that model protection and resource allocation problems on networks. Among them, $[k]$ -Roman domination…

math.CO2026

Further results on $[k]$-Roman domination on cylindrical grids $C_m \Box P_n$

Simon Brezovnik, Janez Žerovnik

In this paper, we study the $[k]$ -Roman domination number of cylindrical graphs $C_{m} □ P_{n}$ . Our analysis begins with a general lower bound based on local neighborhood constrain…

math.CO2026

$[k]$ -Roman domination on cylindrical grids $C_{m} □ P_{n}$

Simon Brezovnik, Janez Žerovnik

Roman domination and its higher-order extensions have attracted considerable attention due to their natural interpretation in terms of defensive resource allocation on networks. Th…

math.CO2024

The 2-rainbow domination number of Cartesian product of cycles

Simon Brezovnik, Darja Rupnik Poklukar, Janez Žerovnik

A $k$ -rainbow dominating function ( $k$ RDF) of $G$ is a function that assigns subsets of ${1, 2, ..., k}$ to the vertices of $G$ such that for vertices $v$ with $f (v) = \emptyset$ we…

Upper bounds for double Roman domination and [k]-Roman domination of cylindrical graphs Cm​□Pn​

Further results on \([k]\)-Roman domination on cylindrical grids \(C_m \Box P_n\)

[k]-Roman domination on cylindrical grids Cm​□Pn​

The 2-rainbow domination number of Cartesian product of cycles

Upper bounds for double Roman domination and $[k]$ -Roman domination of cylindrical graphs $C_{m} □ P_{n}$

$[k]$ -Roman domination on cylindrical grids $C_{m} □ P_{n}$