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2023•Linear Algebra and its ApplicationsOpen access

On signed graphs with at most two eigenvalues unequal to ±1

Willem H. Haemers, Hatice Topçu

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Abstract

We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching.

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What this paper is about

We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching.

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Available abstract

We present the first steps towards the determination of the signed graphs for which the adjacency matrix has all but at most two eigenvalues equal to ±1. Here we deal with the disconnected, the bipartite and the complete signed graphs. In addition, we present many examples which cannot be obtained from an unsigned graph or its negative by switching.

Key concepts: Signed graph, Mathematics, Adjacency matrix, Bipartite graph, Eigenvalues and eigenvectors, Combinatorics, Two-graph, Discrete mathematics

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