TY - JOUR
ID - 14168
TI - Þ-energy of generalized Petersen graphs
JO - Communications in Combinatorics and Optimization
JA - CCO
LA - en
SN - 2538-2128
AU - Joshi, Prajakta Bharat
AU - Joseph, Mayamma
AD - Research scholar, Department of mathematics, CHRIST (Deemed to be University), Bangalore, India
AD - Department of mathematics, Faculty, CHRIST (Deemed to be University), Bangalore.
Y1 - 2022
PY - 2022
VL - 7
IS - 1
SP - 1
EP - 16
KW - Graph energy
KW - partition matrix
KW - Þ-matrix
KW - vertex partitions
DO - 10.22049/cco.2021.27102.1197
N2 - 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.
UR - http://comb-opt.azaruniv.ac.ir/article_14168.html
L1 - http://comb-opt.azaruniv.ac.ir/article_14168_650b69137e573da2101f8309df73ca34.pdf
ER -