C. Elphick

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20242026

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5 papers · 1 filter

math.CO2026

Proof of a conjectured spectral upper bound on the chromatic number of a graph

Quanyu Tang, Clive Elphick

Let $G$ be a simple graph on $n$ vertices and $m$ edges with chromatic number $I ¨ $ , and let $I^»_{n}$ denote the least adjacency eigenvalue. Solving a conjecture of Fan, Yu and Wang~[…

math.CO2025

A new conjecture on the inertia of graphs

Saieed Akbari, Clive Elphick, Hitesh Kumar +2

Let $G$ be a graph with adjacency matrix $A (G)$ . We conjecture that \[2n^+(G) \le n^-(G)(n^-(G) + 1),\] where $n^{+} (G)$ and $n^{-} (G)$ denote the number of positive and negative eigen…

math.CO2025

Inertia, Independence and Expanders

Quanyu Tang, Shengtong Zhang, Clive Elphick

Let $G$ be a graph on $n$ vertices, independence number $I^\pm (G)$ , LovÃ¡sz theta function $ϑ (G)$ , and Shannon capacity $I^ (G)$ . We define $n_{\geq 0} (G)$ to be the minimum numb…

math.CO2025

A Spectral Lower Bound on Chromatic Numbers using $p$ -Energy

Clive Elphick, Quanyu Tang, Shengtong Zhang

Let $A_{G}$ be the adjacency matrix of a simple graph $G$ , and let $I ¨ (G)$ , $I ¨ _{f} (G)$ , $I ¨ _{q} (G)$ , $I^¾ (G)$ and $I^¾_{f} (G)$ denote its chromatic number, fractional chromatic…

math.CO2024

Symmetry and asymmetry between positive and negative square energies of graphs

Clive Elphick, William Linz

The positive and negative square energies of a graph, $s^{+} (G)$ and $s^{-} (G)$ , are the sums of squares of the positive and negative eigenvalues of the adjacency matrix, respectively.…

Proof of a conjectured spectral upper bound on the chromatic number of a graph

A new conjecture on the inertia of graphs

Inertia, Independence and Expanders

A Spectral Lower Bound on Chromatic Numbers using p-Energy

Symmetry and asymmetry between positive and negative square energies of graphs

A Spectral Lower Bound on Chromatic Numbers using $p$ -Energy