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October 2015 A new class of reconstructible graphs from some neighbourhood conditions
Tetsuya HOSAKA, Yonghuo XIAO
Hokkaido Math. J. 44(3): 327-340 (October 2015). DOI: 10.14492/hokmj/1470053367

Abstract

In this paper, we provide a new class of reconstructible finite graphs. We show the following theorem: Let k be a positive integer number. Let Γ be a finite graph with at least 3 vertices. Suppose that Γ satisfies the following two conditions: (i) for any two distinct vertices w,w′ ∈ V(Γ), [w,w′] ∈ E(Γ) ⬄ N(w)-{w′} ≇ N(s) for any vertex sV(Γ); (ii) there exists a vertex vV(Γ) of degree k such that for any k-vertices v1, v2, …, vkV(Γ)-{v}, there exists a vertex uV(Γ) such that St2(u,Γ) ⋂ {v, v1, v2, …, vk} = ∅, where N(w) is the full subgraph of Γ whose vertex set is {vV(Γ)|[w,v] ∈ E(Γ)} and St2(u,Γ) = ⋂ {St(w,Γ)| wV(St(u,Γ))}. Then the graph Γ is reconstructible. We also provide some applications and examples.

Citation

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Tetsuya HOSAKA. Yonghuo XIAO. "A new class of reconstructible graphs from some neighbourhood conditions." Hokkaido Math. J. 44 (3) 327 - 340, October 2015. https://doi.org/10.14492/hokmj/1470053367

Information

Published: October 2015
First available in Project Euclid: 1 August 2016

zbMATH: 1333.05204
MathSciNet: MR3532112
Digital Object Identifier: 10.14492/hokmj/1470053367

Subjects:
Primary: 05C10, 57M15

Rights: Copyright © 2015 Hokkaido University, Department of Mathematics

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Vol.44 • No. 3 • October 2015
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