<abstract xmlns="http://www.w3.org/1999/xhtml">Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions.</abstract>

Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of 𝒫-eigenvalues of 𝒫-matrix of G. Apart from studying some properties of 𝒫-matrix, its eigenvalues and obtaining bounds of 𝒫-energy, we explore the robust(shear) 𝒫-energy which is the maximum(minimum) value of 𝒫-energy for some families of graphs. Further, we derive explicit formulas for E𝒫 (G) of few classes of graphs with different vertex partitions.

𝒫-energy of graphs

prajaktabharat.joshi@res.christuniversity.in

Acta Universitatis Sapientiae, Informatica

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"𝒫-energy of graphs"}

Given a graph G = (V, E), with respect to a vertex partition 𝒫 we associate a matrix called 𝒫-matrix and define the 𝒫-energy, E𝒫 (G) as the sum of...

𝒫-energy of graphs

Published Online: Jul 16, 2020

Page range: 137 - 157

Received: Apr 23, 2020

Accepted: Jun 10, 2020

DOI: https://doi.org/10.2478/ausi-2020-0009

Keywords
graph energy, vertex partitions, k-partition matrix, k-partition energy

© 2020 Prajakta Bharat Joshi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

𝒫-energy of graphs

Published Online: Jul 16, 2020

Page range: 137 - 157

Received: Apr 23, 2020

Accepted: Jun 10, 2020

DOI: https://doi.org/10.2478/ausi-2020-0009

Keywordsgraph energy, vertex partitions, k-partition matrix, k-partition energy

© 2020 Prajakta Bharat Joshi et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
graph energy, vertex partitions, k-partition matrix, k-partition energy