4 citations · 6 across the 12 of their papers we have counts for
15 papers
Stronger Spectral Bound for Clique Number
Hareshkumar Jadav, Sudipta Mallik, Akhilesh Panchangam +1
Given an integer , deciding whether a graph has a clique of size is an NP-complete problem. Wilf's inequality provides a spectral lower bound for the clique number of a grap…
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…
Codes from incidence matrices of hypergraphs
Sudipta Mallik, Bahattin Yildiz
Binary codes are constructed from incidence matrices of hypergraphs. A combinatroial description is given for the minimum distances of such codes via a combinatorial tool called ``…
Matrix tree theorem for the net Laplacian matrix of a signed graph
Sudipta Mallik
For a simple signed graph with the adjacency matrix and net degree matrix , the net Laplacian matrix is . We introduce a new oriented incidence…
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…
Isodual and Self-dual Codes from Graphs
Sudipta Mallik, Bahattin Yildiz
Binary linear codes are constructed from graphs, in particular, by the generator matrix where is the adjacency matrix of a graph on vertices. A combinatorial inte…
An Analog of Matrix Tree Theorem for Signless Laplacians
Keivan Hassani Monfared, Sudipta Mallik
A spanning tree of a graph is a connected subgraph on all vertices with the minimum number of edges. The number of spanning trees in a graph is given by Matrix Tree Theorem in…
Spectral characterization of matchings in graphs
Keivan Hassani Monfared, Sudipta Mallik
A spectral characterization of the matching number (the size of a maximum matching) of a graph is given. More precisely, it is shown that the graphs G of order n whose matching num…
The maximum multiplicity of an eigenvalue of symmetric matrices with a given graph
Keivan Hassani Monfared, Sudipta Mallik
For a graph G, M(G) denotes the maximum multiplicity occurring of an eigenvalue of a symmetric matrix whose zero-nonzero pattern is given by edges of G. We introduce two combinator…
Construction of real skew-symmetric matrices from interlaced spectral data and graph
Keivan Hassani Monfared, Sudipta Mallik
A 1989 result of Duarte asserts that for a given tree T on n vertices, a fixed vertex i, and two sets of distinct real numbers L, M of sizes n and n-1, respectively, such that M st…
Alternative Proofs on the Indices of Cacti and Unicyclic Graphs with Vertices
Sudipta Mallik
Let be the cactus obtained from the star by adding independent edges between pairs of pendant vertices. Let be the un…