2 citations · 2 across the 6 of their papers we have counts for
9 papers · 1 filter
Combinatorial formula for the Moore-Penrose inverse of the complex signless Laplacian of an oriented graph
XiaoYang Liu, Sudipta Mallik, Anh Tang
We find necessary and sufficient conditions for the rank of the signless incidence matrix of a weakly connected oriented graph with non-zero complex edge weights. We use this to fi…
Signed graphs and inverses of their incidence matrices
Abdullah Alazemi, Milica Andelic, Sudipta Mallik
The Laplacian matrix of a signed graph may or may not be invertible. We present a combinatorial formula of the Moore-Penrose inverse of . This is achieved by finding a c…
Incidence and Laplacian matrices of wheel graphs and their inverses
Jerad Ipsen, Sudipta Mallik
It has been an open problem to find the Moore-Penrose inverses of the incidence, Laplacian, and signless Laplacian matrices of families of graphs except trees and unicyclic graphs.…
The Inverse of the Incidence Matrix of a Unicyclic Graph
Ryan Hessert, Sudipta Mallik
The vertex-edge incidence matrix of a (connected) unicyclic graph G is a square matrix which is invertible if and only if the cycle of G is an odd cycle. A combinatorial formula of…
A New Formula for the Minimum Distance of an Expander Code
Sudipta Mallik
An expander code is a binary linear code whose parity-check matrix is the bi-adjacency matrix of a bipartite expander graph. We provide a new formula for the minimum distance of su…
Moore-Penrose Inverses of the Signless Laplacian and Edge-Laplacian of Graphs
Ryan Hessert, Sudipta Mallik
The signless Laplacian Q and signless edge-Laplacian S of a given graph may or may not be invertible. The Moore-Penrose inverses of Q and S are studied. In particular, using the in…