arXiv subjects

Sayinath Udupa N. V

Publications and source records attributed to Sayinath Udupa N. V.

4 recordsLinked to original sources

arXiv2026

Extremal Graphs with Prescribed Parameters for the Spectral Radius of Weighted Adjacency Matrices with Property $P^{\ast}$

In the literature, several graph matrices based on vertex degrees have been introduced, and the study of their spectral properties has attracted considerable attention in recent years. Motivated by these developments, in this paper, we investigate the spectral radius of the weighted adjacency matrix $A_f(G)$, where the function $f$ satisfies property $P^{*}$. More precisely, we characterize the graphs that attain the maximum spectral radius of $A_f(G)$ among graphs with a vertex cut set of prescribed order, graphs with exactly $s$ cut edges, and graphs with given vertex connectivity and independence number. Our results further develop the unified framework for studying extremal spectral properties of degree-based weighted adjacency matrices and extend this framework to several classes of graphs with prescribed structural parameters.

math.CO↗

arXiv2025

On extremal graphs with respect to the ABS index

Recently, Ali et al. posed several open problems concerning extremal graphs with respect to the ABS index. These problems involve characterizing graphs that attain the maximum ABS index within specific graph classes, including: connected graphs with n vertices and p cut-vertices; (ii) connected graphs of order n with vertex k-partiteness; and (iii) connected bipartite graphs of order n with a fixed vertex connectivity κ. In this paper, we provide complete solutions to all of these problems.

math.CO↗

arXiv2025

Extremal $ABS$ Spectral Radius in Bicyclic and Bipartite Unicyclic Graphs

The ABS spectral radius of a graph G is defined as the largest eigenvalue of its $ABS$ matrix. Motivated by recent studies on this parameter, in this paper, we determine the bipartite unicyclic graphs that attain the largest $ABS$ spectral radius. Furthermore, we characterize the bicyclic graphs that attain the largest and the second largest $ABS$ spectral radii.

math.CO↗

arXiv2024

On the $\mathcal{ABS}$ spectrum and energy of graphs

Let $η_{1}\ge η_{2}\ge\cdots\ge η_{n}$ be the eigenavalues of $\mathcal{ABS}$ matrix. In this paper, we characterize connected graphs with $\mathcal{ABS}$ eigenvalue $η_{n}>-1$. 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.

math.CO↗