DisCoMath Seminar
On the 𝑛-attack Roman Dominating Number of a Graph and the
use of End-Connected Center-Disjoint P5
subgraphs
Garrison
Koch
Rochester Institute of
Technology
Abstract:
The Roman Dominating number is a widely studied
variant of the dominating number on graphs. Given a graph
𝐺=(𝑉,𝐸), the dominating number of a graph is the minimum
size of a vertex set, 𝑉′⊆𝑉, so that every vertex in the graph is either in
𝑉′ or is adjacent to a vertex in
𝑉′. The Roman Dominating function of
𝐺 is defined as 𝑓:𝑉→{0,1,2} such that every vertex with a label of 0
in 𝐺 is adjacent to a vertex with a label of 2. The Roman
Dominating number of a graph is the minimum total weight over all
possible Roman Dominating functions. In this talk we analyze a new
variant: 𝑛-attack Roman Domination, particularly focusing on
2-attack Roman Domination (𝑛=2). The 𝑛-attack Roman Dominating function of
𝐺 is defined similarly to the Roman Dominating
function with the additional condition that for any
𝑗≤𝑛, any subset 𝑆 of 𝑗 vertices all with label 0, must have at least
𝑗 vertices with label 2 in the open neighborhood of
𝑆. The 𝑛-attack Roman Dominating number is the minimum total
weight over all possible 𝑛-attack Roman Dominating functions. We introduce a
method for finding the 2RD number of a graph. We touch on extensions such
as infinite regular graphs and "finite resources". We conclude with open
questions and possible ways to extend these results to the general
𝑛-attack case.
Keep up with DisCoMath Seminars on the DisCoMathS webpage.
Intended Audience:
All are welcome.
To request an interpreter, please visit myaccess.rit.edu
Event Contact:
Brendan Rooney | brsma@rit.edu
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