3 papers
math.CO2026
Upper bounds for double Roman domination and -Roman domination of cylindrical graphs
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, -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 -Roman domination number of cylindrical graphs . Our analysis begins with a general lower bound based on local neighborhood constrain…
math.CO2026
-Roman domination on cylindrical grids
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…