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(t,r) Broadcast Domination Numbers and Densities of the Truncated Square Tiling Graph

2024/08/23 by Cervantes, Jillian, Harris, Pamela E.
#05C12 #05C69 #68R05 #68R10 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.13331

Abstract

For a pair of positive integer parameters (t,r), a subset T of vertices of a graph G is said to (t,r) broadcast dominate a graph G if, for any vertex u in G, we have ∑v∈ T, u∈ Nt(v)(t-d(u,v))≥ r, where where Nt(v)=\u∈ V:d(u,v)

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