Search Results - "Bapat, R.B."

ON THE LAPLACIAN SPECTRA OF PRODUCT GRAPHS by Barik, S., Bapat, R. B., Pati, S.

“…Graph products and their structural properties have been studied extensively by many researchers. We investigate the Laplacian eigenvalues and eigenvectors of…”
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On the adjacency matrix of a block graph by Bapat, R.B., Roy, Souvik

“…A block graph is a graph in which every block is a complete graph. Let be a block graph and let be the adjacency matrix of . We first obtain a formula for the…”
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On the first passage time of a simple random walk on a tree by Bapat, R.B.

“…We consider a simple random walk on a tree. Exact expressions are obtained for the expectation and the variance of the first passage time, thereby recovering…”
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On algebraic connectivity of graphs with at most two points of articulation in each block by Bapat, R.B., Lal, A.K., Pati, S.

“…Let G be a connected graph and let L(G) be its Laplacian matrix. We show that given a graph G with a point of articulation u, and a spanning tree T, there is a…”
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On the adjacency matrix of a threshold graph by Bapat, R.B.

“…A threshold graph on n vertices is coded by a binary string of length n−1. We obtain a formula for the inertia of (the adjacency matrix of) a threshold graph…”
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Squared distance matrix of a tree: Inverse and inertia by Bapat, R.B., Sivasubramanian, Sivaramakrishnan

“…Let T be a tree with vertices V(T)={1,…,n}. The distance between vertices i,j∈V(T), denoted dij, is defined to be the length (the number of edges) of the path…”
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Inverses of triangular matrices and bipartite graphs by Bapat, R.B., Ghorbani, E.

“…To a given nonsingular triangular matrix A with entries from a ring, we associate a weighted bipartite graph G(A) and give a combinatorial description of the…”
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The bipartite distance matrix of a nonsingular tree by Bapat, R.B., Jana, Rakesh, Pati, S.

“…Let G be a labeled, connected, bipartite graph with the bi-partition (L={l1,…,lk},R={r1,…,rp}) of the vertex set V. Let D be the usual distance matrix of G,…”
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An inverse formula for the distance matrix of a wheel graph with an even number of vertices by Balaji, R., Bapat, R.B., Goel, Shivani

“…Let n≥4 be an even integer and Wn be the wheel graph with n vertices. The distance dij between any two distinct vertices i and j of Wn is the length of the…”
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Generalized Euclidean distance matrices by Balaji, R., Bapat, R.B., Goel, Shivani

“…Euclidean distance matrices ( ) are symmetric nonnegative matrices with several interesting properties. In this article, we introduce a wider class of matrices…”
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Resistance matrices of balanced directed graphs by Balaji, R., Bapat, R.B., Goel, Shivani

“…Let G be a strongly connected and balanced directed graph. We define the resistance between any two vertices i and j of G by using the Moore-Penrose inverse of…”
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Resistance distance of blowups of trees by Azimi, A., Bapat, R.B., Farrokhi D.G., M.

“…A blowup of a graph Γ with respect to a graph Γ′ is the graph ΓΓ′ obtained from Γ by replacing every vertex u of Γ with a disjoint copy Γu′ of Γ′ and attach…”
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Product distance matrix of a tree with matrix weights by Bapat, R.B., Sivasubramanian, Sivaramakrishnan

“…Let T be a tree on n vertices and let the n−1 edges e1,e2,…,en−1 have weights that are s×s matrices W1,W2,…,Wn−1, respectively. For two vertices i, j, let the…”
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Corrigendum to “Generalized principal pivot transform” [Linear Algebra Appl. 454 (2014) 49–56] by Rajesh Kannan, M., Bapat, R.B.

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On weighted directed graphs by Bapat, R.B., Kalita, D., Pati, S.

“…The study of a mixed graph and its Laplacian matrix have gained quite a bit of interest among the researchers. Mixed graphs are very important for the study of…”
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On minors of the compound matrix of a Laplacian by Bapat, R.B.

“…Let L be an n×n matrix with zero row and column sums, n⩾3. We obtain a formula for any minor of the (n−2)-th compound of L. An application to counting spanning…”
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Convex and quasiconvex functions on trees and their applications by Bapat, R.B., Kalita, D., Nath, M., Sarma, D.

“…We introduce convex and quasiconvex functions on trees and prove that for a tree the eccentricity, transmission and weight functions are strictly quasiconvex…”
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Identities for minors of the Laplacian, resistance and distance matrices by Bapat, R.B., Sivasubramanian, Sivaramakrishnan

“…It is shown that if L and D are the Laplacian and the distance matrix of a tree respectively, then any minor of the Laplacian equals the sum of the cofactors…”
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PRODUCT DISTANCE MATRIX OF A GRAPH AND SQUARED DISTANCE MATRIX OF A TREE by Bapat, R. B., Sivasubramanian, S.

“…Let G be a strongly connected, weighted directed graph. We define a product distance η(i, j) for pairs i, j of vertices and form the corresponding product…”
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Self-inverse unicyclic graphs and strong reciprocal eigenvalue property by Bapat, R.B., Panda, S.K., Pati, S.

“…We consider only simple graphs. A graph G is said to be nonsingular if its adjacency matrix A(G) is nonsingular. The inverse of a nonsingular graph G is the…”
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