| dc.contributor.author |
Nandi, Raju |
|
| dc.coverage.spatial |
United States of America |
|
| dc.date.accessioned |
2023-04-21T14:50:46Z |
|
| dc.date.available |
2023-04-21T14:50:46Z |
|
| dc.date.issued |
2023-04 |
|
| dc.identifier.citation |
Nandi, Raju, "Group inverses of weighted trees", arXiv, Cornell University Library, DOI: arXiv:2304.03020, Apr. 2023. |
|
| dc.identifier.uri |
https://arxiv.org/abs/2304.03020v1 |
|
| dc.identifier.uri |
https://repository.iitgn.ac.in/handle/123456789/8763 |
|
| dc.description.abstract |
Let (G,w) be an undirected weighted graph. The group inverse of (G,w) is the weighted graph with the adjacency matrix A#, where A is the adjacency matrix of (G,w). We study the group inverse of singular weighted trees. It is shown that if (T,w) is a singular weighted tree, then T# is again a tree, if and only if T is a star tree, which in turn, holds if and only if T# is graph isomorphic to T. A new class T of weighted trees, is introduced and studied here. It is shown that the group inverse of the adjacency matrix of a positively weighted tree in T, is signature similar to a non-negative matrix. |
|
| dc.description.statementofresponsibility |
by Raju Nandi |
|
| dc.language.iso |
en_US |
|
| dc.publisher |
Cornell University Library |
|
| dc.subject |
Weighted graph |
|
| dc.subject |
Adjacency matrix |
|
| dc.subject |
Inverse of graph |
|
| dc.subject |
Maximum matching |
|
| dc.subject |
Alternating path |
|
| dc.title |
Group inverses of weighted trees |
|
| dc.type |
Pre-Print Archive |
|
| dc.relation.journal |
arXiv |
|