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pro vyhledávání: '"Kannan, M. Rajesh"'
In 2010, Butler introduced the unfolding operation on a bipartite graph to produce two bipartite graphs, which are cospectral for the adjacency and the normalized Laplacian matrices. In this article, we describe how the idea of unfolding a bipartite
Externí odkaz:
http://arxiv.org/abs/2401.03035
Autor:
Samanta, Aniruddha, Kannan, M. Rajesh
A complex unit gain graph ($ \mathbb{T} $-gain graph), $ \Phi=(G, \varphi) $ is a graph where the gain function $ \varphi $ assigns a unit complex number to each orientation of an edge of $ G $ and its inverse is assigned to the opposite orientation.
Externí odkaz:
http://arxiv.org/abs/2312.17152
Autor:
Mahato, Iswar, Kannan, M. Rajesh
In this article, we show that the generalized tree shift operation increases the distance spectral radius, distance signless Laplacian spectral radius, and the $D_\alpha$-spectral radius of complements of trees. As a consequence of this result, we co
Externí odkaz:
http://arxiv.org/abs/2306.05155
Autor:
Mahato, Iswar, Kannan, M. Rajesh
The eccentricity matrix of a connected graph $G$, denoted by $\mathcal{E}(G)$, is obtained from the distance matrix of $G$ by keeping the largest nonzero entries in each row and each column, and leaving zeros in the remaining ones. The $\mathcal{E}$-
Externí odkaz:
http://arxiv.org/abs/2301.01708
Autor:
Mahato, Iswar, Kannan, M. Rajesh
The eccentricity matrix of a connected graph $G$, denoted by $\mathcal{E}(G)$, is obtained from the distance matrix of $G$ by keeping the largest nonzero entries in each row and each column and leaving zeros in the remaining ones. The eigenvalues of
Externí odkaz:
http://arxiv.org/abs/2208.13462
Autor:
Mahato, Iswar, Kannan, M. Rajesh
Let $T$ be a tree on $n$ vertices whose edge weights are positive definite matrices of order $s$. The squared distance matrix of $T$, denoted by $\Delta$, is the $ns \times ns$ block matrix with $\Delta_{ij}=d(i,j)^2$, where $d(i,j)$ is the sum of th
Externí odkaz:
http://arxiv.org/abs/2205.01734
A signed graph $\Sigma = (G, \sigma)$ is a graph where the function $\sigma$ assigns either $1$ or $-1$ to each edge of the simple graph $G$. The adjacency matrix of $\Sigma$, denoted by $A(\Sigma)$, is defined canonically. In a recent paper, Wang et
Externí odkaz:
http://arxiv.org/abs/2204.09870
Autor:
Mahato, Iswar, Kannan, M. Rajesh
The \textit{eccentricity matrix} $\mathcal{E}(G)$ of a connected graph $G$ is obtained from the distance matrix of $G$ by keeping the largest non-zero entries in each row and each column, and leaving zeros in the remaining ones. The eigenvalues of $\
Externí odkaz:
http://arxiv.org/abs/2203.16186
Publikováno v:
Discrete Mathematics 345 (8), 112916 (2024)
In this article, we construct bipartite graphs which are cospectral for both the adjacency and normalized Laplacian matrices using partitioned tensor product. This extends the construction of Ji, Gong, and Wang \cite{ji-gong-wang}. Our proof of the c
Externí odkaz:
http://arxiv.org/abs/2110.09034
Autor:
Mahato, Iswar, Kannan, M. Rajesh
The eccentricity matrix $\varepsilon(G)$ of a graph $G$ is obtained from the distance matrix of $G$ by retaining the largest distances in each row and each column, and leaving zeros in the remaining ones. The eccentricity energy of $G$ is sum of the
Externí odkaz:
http://arxiv.org/abs/2107.03237