Spectral properties of eccentricity sum matrix of graphs

Articles in Press

Document Type : Original paper

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Department of Mathematics, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal-576-104, Karnataka, India

Abstract

The spectral properties of extended adjacency matrices possess high discriminating power and correlate well with various physicochemical properties and biological activities of organic compounds. In the current article, a detailed investigation of one of the extended adjacency matrices called the eccentricity sum matrix is undertaken. The eccentricity sum matrix of a graph G, denoted by A_(ε^c ) (G) is a real symmetric matrix that if i≠ j and v_i v_j∈ E(G), then the (i,j)^th- entry is e(v_i)+e(v_j) and zero otherwise, where e(v_i) is the eccentricity of vertex v_i. The properties like trace, principle minors, and eigenvalues of the eccentricity sum matrix are explored. Moreover, we present some bounds for spectral radius and energy. Also, the energy and spectrum of some classes of graphs like fan graphs, bi-star graphs, etc., and their complements are obtained.

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References

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Communications in Combinatorics and Optimization

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Available Online from 10 June 2025

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