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Joyentanuj Das

Publications and source records attributed to Joyentanuj Das.

22 records · Page 2Linked to original sources
arXiv2020

On the spectral radius of bi-block graphs with given independence number $α$

A connected graph is called a bi-block graph if each of its blocks is a complete bipartite graph. Let $\mathcal{B}(\mathbf{k}, α)$ be the class of bi-block graph on $\mathbf{k}$ vertices with given independence number $α$. It is easy to see that every bi-block graph is a bipartite graph. For a bipartite graph $G$ on $\mathbf{k}$ vertices, the independence number $α(G)$ satisfies $\ceil*{\frac{\mathbf{k}}{2}} \leq α(G) \leq \mathbf{k}-1$. In this article, we prove that the maximum spectral radius $ρ(G)$ among all graphs $G$ in $\mathcal{B}(\mathbf{k}, α)$, is uniquely attained for the complete bipartite graph $K_{α, \mathbf{k}-α}$.

math.CO↗
arXiv2020

Distance Matrix of Weighted Cactoid-type Digraphs

A strongly connected digraph is called a cactoid-type if each of its blocks is a digraph consisting of finitely many oriented cycles sharing a common directed path. In this article, we find the formula for the determinant of the distance matrix for weighted cactoid-type digraphs and find its inverse, whenever it exists. We also compute the determinant of the distance matrix for a class of unweighted and undirected graphs consisting of finitely many cycles, sharing a common path.

math.CO↗
arXiv2020

Distance Matrix of a Class of Completely Positive Graphs: Determinant and Inverse

A real symmetric matrix $A$ is said to be completely positive if it can be written as $BB^t$ for some (not necessarily square) nonnegative matrix $B$. A simple graph $G$ is called a completely positive graph if every doubly nonnegative matrix realization of $G$ is a completely positive matrix. Our aim in this manuscript is to compute the determinant and inverse (when it exists) of the distance matrix of a class of completely positive graphs. Similar to trees, we obtain a relation for the inverse of the distance matrix of a class of completely positive graphs involving the Laplacian matrix, a rank one matrix and a matrix $\mathcal{R}$. We also determine the eigenvalues of some principal submatrices of matrix $\mathcal{R}$.

math.CO↗