On total isolation in graphs

Geoffrey Boyer; Wayne Goddard; Michael A. Henning

doi:10.1007/s00010-024-01057-1

On total isolation in graphs

Geoffrey Boyer
, Wayne Goddard
, Michael A. Henning

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

An isolating set in a graph is a set S of vertices such that removing S and its neighborhood leaves no edge; it is total isolating if S induces a subgraph with no vertex of degree 0. We show that most graphs have a partition into two disjoint total isolating sets and characterize the exceptions. Using this we show that apart from the 7-cycle, every connected graph of order n≥4 has a total isolating set of size at most n/2, which is best possible.

Original language	English
Pages (from-to)	623-633
Number of pages	11
Journal	Aequationes Mathematicae
Volume	99
Issue number	2
DOIs	https://doi.org/10.1007/s00010-024-01057-1
Publication status	Published - Apr 2025

ASJC Scopus subject areas

General Mathematics
Discrete Mathematics and Combinatorics
Applied Mathematics

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10.1007/s00010-024-01057-1

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abstract = "An isolating set in a graph is a set S of vertices such that removing S and its neighborhood leaves no edge; it is total isolating if S induces a subgraph with no vertex of degree 0. We show that most graphs have a partition into two disjoint total isolating sets and characterize the exceptions. Using this we show that apart from the 7-cycle, every connected graph of order n≥4 has a total isolating set of size at most n/2, which is best possible.",

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On total isolation in graphs

Abstract

ASJC Scopus subject areas

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