Let $\eta_{1}\ge \eta_{2}\ge\cdots\ge \eta_{n}$ be the eigenvalues of $\mathcal{ABS}$ matrix. In this paper, we characterize connected graphs with $\mathcal{ABS}$ eigenvalue $\eta_{n}>-1$. As a result, we determine all connected graphs with exactly two distinct $\mathcal{ABS}$ eigenvalues. We show that a connected bipartite graph has three distinct $\mathcal{ABS}$ eigenvalues if and only if it is a complete bipartite graph. Furthermore, we present some bounds for the $\mathcal{ABS}$ spectral radius (resp. $\mathcal{ABS}$ energy) and characterize extremal graphs. Also, we obtain a relation between $\mathcal{ABC}$ energy and $\mathcal{ABS}$ energy. Finally, the chemical importance of $\mathcal{ABS}$ energy is investigated and it shown that the $\mathcal{ABS}$ energy is useful in predicting certain properties of molecules.
Shetty, S. , Rakshith, B. and Udupa N V, S. (2025). On the ABS spectrum and energy of graphs. Communications in Combinatorics and Optimization, (), -. doi: 10.22049/cco.2025.30274.2603
MLA
Shetty, S. , , Rakshith, B. , and Udupa N V, S. . "On the ABS spectrum and energy of graphs", Communications in Combinatorics and Optimization, , , 2025, -. doi: 10.22049/cco.2025.30274.2603
HARVARD
Shetty, S., Rakshith, B., Udupa N V, S. (2025). 'On the ABS spectrum and energy of graphs', Communications in Combinatorics and Optimization, (), pp. -. doi: 10.22049/cco.2025.30274.2603
CHICAGO
S. Shetty , B. Rakshith and S. Udupa N V, "On the ABS spectrum and energy of graphs," Communications in Combinatorics and Optimization, (2025): -, doi: 10.22049/cco.2025.30274.2603
VANCOUVER
Shetty, S., Rakshith, B., Udupa N V, S. On the ABS spectrum and energy of graphs. Communications in Combinatorics and Optimization, 2025; (): -. doi: 10.22049/cco.2025.30274.2603
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