Zobrazeno 1 - 10
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pro vyhledávání: '"Bapat, Ravindra B."'
Publikováno v:
Special Matrices, Vol 11, Iss 1, Pp 21-33 (2023)
For a bipartite graph, the complete adjacency matrix is not necessary to display its adjacency information. In 1985, Godsil used a smaller size matrix to represent this, known as the bipartite adjacency matrix. Recently, the bipartite distance matrix
Externí odkaz:
https://doaj.org/article/845639d6ddc64ef9848ec28f4dd8cc8c
Let $G=(V,E)$ be a strongly connected and balanced digraph with vertex set $V=\{1,\dotsc,n\}$. The classical distance $d_{ij}$ between any two vertices $i$ and $j$ in $G$ is the minimum length of all the directed paths joining $i$ and $j$. The resist
Externí odkaz:
http://arxiv.org/abs/1911.05951
Autor:
Bapat, Ravindra B.
Let $T$ be a tree with vertex set $\{1, \ldots, n\}$ such that each edge is assigned a nonzero weight. The squared distance matrix of $T,$ denoted by $\Delta,$ is the $n \times n$ matrix with $(i,j)$-element $d(i,j)^2,$ where $d(i,j)$ is the sum of t
Externí odkaz:
http://arxiv.org/abs/1810.06182
The \emph{resistance matrix} of a simple connected graph $G$ is denoted by $R$, and is defined by $R =(r_{ij})$, where $r_{ij}$ is the resistance distance between the vertices $i$ and $j$ of $G$. In this paper, we consider the resistance matrix of we
Externí odkaz:
http://arxiv.org/abs/1804.01325
Publikováno v:
Special Matrices, Vol 10, Iss 1, Pp 267-284 (2022)
In this article, we show that the rank of the 2-Steiner distance matrix of a caterpillar graph having NN vertices and pp pendant veritices is 2N−p−12N-p-1.
Externí odkaz:
https://doaj.org/article/e2e3cbbdfff74091b5ef86d98dbe1b3c
Autor:
Singh, Ranveer, Bapat, Ravindra B.
In a signed graph $G$, an induced subgraph is called a negative clique if it is a complete graph and all of its edges are negative. In this paper, we give the characteristic polynomials and the eigenvalues of some signed graphs having negative clique
Externí odkaz:
http://arxiv.org/abs/1702.06322
The Kirchhoff index of a graph is defined as half of the sum of all effective resistance distances between any two vertices. Assuming a complete multipartite graph G, by methods from linear algebra we explicitly formulate effective resistance distanc
Externí odkaz:
http://arxiv.org/abs/1611.09457
Autor:
Bapat, Ravindra B.
Nath and Paul (Linear Algebra Appl.,460(2014),97-110) have shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has properties similar to the Fiedler vector. We given an alternative proof, establi
Externí odkaz:
http://arxiv.org/abs/1411.0210
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