On Extended Adjacency Matrices Associated with Eccentricity-Based Topological Indices

Balkishbanu Khaji; Shahistha Hanif; K. Arathi Bhat

doi:10.5269/bspm.78034

Balkishbanu Khaji
Shahistha Hanif Manipal Academy of Higher Education, Manipal
K. Arathi Bhat

Abstract

Several investigations of the extended adjacency matrices associated with various degree-based topological indices have been undertaken in recent years, leading to sharper theorems, improved inequalities, and sometimes non-existent conclusions. Motivated by this, we delve into the section on eccentricity-based topological indices and consider the extended adjacency matrices associated with them. Suppose is a symmetric function associated with an eccentricity-based topological index, then a generalized extended adjacency matrix has entry as the value of at the eccentricities of the corresponding vertices if they are adjacent, else it is 0. The expression and bounds for parameters like the trace, determinant, and eigenvalues associated with this matrix are derived in this article. The expression for the determinant indicates that it depends on the number of elementary spanning subgraphs present in the graph. Several bounds for the largest eigenvalue of are derived in terms of the diameter order and size of the graph. One of them is , with equality in the case of complete graphs.

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