@article { author = {Joshi, Prajakta and Joseph, Mayamma}, title = {Þ-energy of generalized Petersen graphs}, journal = {Communications in Combinatorics and Optimization}, volume = {7}, number = {1}, pages = {1-16}, year = {2022}, publisher = {Azarbaijan Shahid Madani University}, issn = {2538-2128}, eissn = {2538-2136}, doi = {10.22049/cco.2021.27102.1197}, 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.}, keywords = {Graph energy,partition matrix,Þ-matrix,vertex partitions}, url = {http://comb-opt.azaruniv.ac.ir/article_14168.html}, eprint = {http://comb-opt.azaruniv.ac.ir/article_14168_650b69137e573da2101f8309df73ca34.pdf} }