An upper bound for neighbor-connectivity of graphs

Hongliang Ma and Baoyindureng Wu ()
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Hongliang Ma: Xinjiang University
Baoyindureng Wu: Xinjiang University

Journal of Combinatorial Optimization, 2024, vol. 48, issue 5, No 8, 14 pages

Abstract: Abstract The neighbor-connectivity of a graph G, denoted by $$\kappa _{NB}(G)$$ κ NB ( G ) , is the least number of vertices such that removing their closed neighborhoods from G results in a graph that is empty, complete, or disconnected. In the paper, we show that for any graph G of order n, $$\kappa _{NB}(G)\le \lceil \sqrt{2n}\ \rceil -2$$ κ NB ( G ) ≤ ⌈ 2 n ⌉ - 2 . We pose a conjecture that $$\kappa _{NB}(G)\le \lceil \sqrt{n}\ \rceil -1$$ κ NB ( G ) ≤ ⌈ n ⌉ - 1 for a graph G of order n. For supporting it, we show that the conjecture holds for any triangle-free graphs, Cartesian, direct, lexicographic product of any two graphs.

Keywords: Neighbor-connectivity; Triangle-free graphs; Product graphs (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10878-024-01235-6

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