On the minimal energy of tetracyclic graphs

TL;DR

This paper characterizes tetracyclic graphs with minimal energy, confirming a conjecture for graphs with $e=n+3$, and advances understanding of graph energy minimization.

Contribution

It provides a complete characterization of minimal energy tetracyclic graphs and verifies a specific conjecture in the field.

Findings

Identified the tetracyclic graph of order n with minimal energy.

Confirmed the conjecture for the case e=n+3.

Contributed to the theory of graph energy minimization.

Abstract

The energy of a graph is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. In this paper, we characterize the tetracyclic graph of order $n$ with minimal energy. By this, the validity of a conjecture for the case $e=n+3$ proposed by Caporossi et al. \cite{CCGH} has been confirmed.