Þ-energy of generalized Petersen graphs

Document Type : Original paper

Authors

1 Research scholar, Department of mathematics, CHRIST (Deemed to be University), Bangalore, India

2 Department of mathematics, Faculty, CHRIST (Deemed to be University), Bangalore.

Abstract

For a given graph $ G $, its $\mathscr{P}$-energy is the sum of the absolute values of the eigenvalues of the  $\mathscr{P}$-matrix of $ G $. In this article, we explore the $\mathscr{P}$-energy of generalized Petersen graphs $ G(p,k) $ for various vertex partitions such as independent, domatic, total domatic and $ k $-ply domatic partitions and partition containing a perfect matching in $ G(p,k) $. Further, we present a python program to obtain the $\mathscr{P}$-energy of $ G(p,k) $ for the vertex partitions under consideration and examine the relation between them.

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References

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Communications in Combinatorics and Optimization
Volume 7, Issue 1
June 2022
Pages 1-16

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