Year: 2024
Type: article
Abstract: Let G = (V (G), E(G)) be a simple graph with vertex set V (G) and edge set E(G). Let S be a subset of V (G), and let B(S) be the set of neighbours of S in V (G)∖S. The differential ∂(S) of S is the number |B(S)|−|S|. The maximum value of ∂(S) taken over all subsets S ⊆ V (G) is the differential ∂(G) of G. The graph R(G) is defined as the graph obtained from G by adding a new vertex ve for each e ∈ E(G), and by joining ve to the end vertices of e. In this paper we study the relationship between ∂(G) and ∂(R(G)), and give tight asymptotic bounds for ∂(R(G)). We also exhibit some relationships between certain vertex sets of G and R(G) which involve well known graph theoretical parameters.
Source: RAIRO - Operations Research
DOI: 10.1051/ro/2024212
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4404081619