The power graph of a finite group is defined to be the graph whose vertex set is and in which two distinct vertices are adjacent if and only if or for some positive integers . The distance signless Laplacian matrix of a graph , denoted by , is defined as , where is the distance matrix of and is the transmission matrix of . We determine the distance signless Laplacian eigenvalues of the power graphs of the finite cyclic group and the dihedral group . We provide upper and lower bounds on the largest eigenvalue of the distance signless Laplacian matrix of and . We also give a short proof of the lower bound on the algebraic connectivity of obtained by Chattopadhyay and Panigrahi (Linear and Multilinear Algebra 63:7 (2015), 1345–1355).
"ON SPECTRA OF POWER GRAPHS OF FINITE CYCLIC AND DIHEDRAL GROUPS." Rocky Mountain J. Math. 53 (2) 341 - 356, April 2023. https://doi.org/10.1216/rmj.2023.53.341