On (distance) signless Laplacian spectra of graphs

Rakshith, B. R.; Das, Kinkar Ch.; Sriraj, M. A.

doi:10.1007/s12190-020-01468-8

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“…The energy E(G) is the sum of absolute A-eigenvalues of G. A significant amount of research has been conducted on this idea [16]. Following the potential applications of the A-spectrum, numerous topological indices were investigated from a spectral perspective by modifying the classical adjacency matrix accordingly [19][20][21][22][23][24][25][26][27][28][29]. Zhou and Trinajstić [30] introduced the matrix corresponding to the sum-connectivity index and studied associated energy in 2010.…”

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confidence: 99%

On Neighborhood Inverse Sum Indeg Energy of Molecular Graphs

et al. 2022

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The spectral graph theory explores connections between combinatorial features of graphs and algebraic properties of associated matrices. The neighborhood inverse sum indeg (NI) index was recently proposed and explored to be a significant molecular descriptor. Our aim is to investigate the NI index from a spectral standpoint, for which a suitable matrix is proposed. The matrix is symmetric since it is generated from the edge connection information of undirected graphs. A novel graph energy is introduced based on the eigenvalues of that matrix. The usefulness of the energy as a molecular structural descriptor is analyzed by investigating predictive potential and isomer discrimination ability. Fundamental mathematical properties of the present spectrum and energy are investigated. The spectrum of the bipartite class of graphs is identified to be symmetric about the origin of the real line. Bounds of the spectral radius and the energy are explained by identifying the respective extremal graphs.

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