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arXiv · 1901.06692

Proof of a Conjecture on the Seidel Energy of Graphs

Saieed Akbari·Mostafa Einollahzadeh·Mohammad Mahdi Karkhaneei·Mohammad Ali Nematollahi
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Abstract

Let $G$ be a graph with the vertex set $ \lbrace v_1,\ldots,v_n \rbrace$. The Seidel matrix of $G$ is an $n\times n$ matrix whose diagonal entries are zero, $ij$-th entry is $-1$ if $ v_{i} $ and $ v_{j} $ are adjacent and otherwise is $ 1 $. The Seidel energy of $G$ is defined to be the sum of absolute values of all eigenvalues of the Seidel matrix of $G$. Haemers conjectured that the Seidel energy of any graph of order $n$ is at least $2n-2$ and, up to Seidel equivalence, the equality holds for $ K_{n} $. We establish the validity of Haemers' Conjecture in general.

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Saieed Akbari, Mostafa Einollahzadeh, Mohammad Mahdi Karkhaneei, Mohammad Ali Nematollahi. 2019-01-20. Proof of a Conjecture on the Seidel Energy of Graphs. https://arxiv.org/abs/1901.06692

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