# DisCoMath Seminar: On the π-attack Roman Dominating Number of a Graph and the use of End-Connected Center-Disjoint P5 subgraphs

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DisCoMath Seminar
On the π-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 πΊ=(π,πΈ), the dominating number of a graph is the minimum size of a vertex set, πβ²βπ, so that every vertex in the graph is either in πβ² or is adjacent to a vertex in πβ². The Roman Dominating function of πΊ is defined as π:πβ{0,1,2} such that every vertex with a label of 0 in πΊ 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: π-attack Roman Domination, particularly focusing on 2-attack Roman Domination (π=2). The π-attack Roman Dominating function of πΊ is defined similarly to the Roman Dominating function with the additional condition that for any πβ€π, any subset π of π vertices all with label 0, must have at least π vertices with label 2 in the open neighborhood of π. The π-attack Roman Dominating number is the minimum total weight over all possible π-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 π-attack case.

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Intended Audience:
All are welcome.

To request an interpreter, please visit myaccess.rit.edu

Event Contact: Brendan Rooney | brsma@rit.eduΒ

Contact
Brendan Rooney
##### Event Snapshot
###### When and Where
February 28, 2024
1:00 pm - 2:00 pm
Room/Location: 1155
###### Who

Open to the Public

No

research