Title of article :
Moore–Penrose Inverse of the Signless Laplacians of Bipartite Graphs
Author/Authors :
Alazemi ، Abdullah Department of Mathematics - Faculty of Science - Kuwait University , Alhalabi ، Osama Department of Mathematics - College of Graduate Studies - Kuwait University , Anđelić ، Milica Department of Mathematics - Faculty of Science - Kuwait University
Abstract :
We provide a relation between theMoore–Penrose inverse of theLaplacian and signless Laplacian matrices of a bipartite graph. As a consequence, we obtain combinatorial formulae for the Moore–Penrose inverse of signless Laplacians of bipartite graphs.We also provide a combinatorial formula for the Moore–Penrose inverse of an incidence matrix of any graph. In this way, we answer some of open problems raised in Hessert and Mallik (Discrete Math 344:112451, 2021).
Keywords :
Moore–Penrose inverse , Incidence matrix , Signless Laplacian matrix , Laplacian matrix ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
