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- Title
SOME RESULTS ON MATRICES WITH RESPECT TO RESISTANCE DISTANCE.
- Authors
JUNHAO ZHANG; XIN ZOU; ZHONGXUN ZHU
- Abstract
The resistance matrix R = R(G) of G is a matrix whose (i, j) -th entry is equal to the resistance distance rG(vi,vj). The resistance Re(vi) of a vertex vi is defined to be the sum of the resistance from vi to all other vertices in G, i.e., Re(vi) = Σnj=1 rG(vi,vj). The resistance signless Laplacian matrix of a connected graph G is defined to be RQ = diag(Re)+R, where diag(Re) is the diagonal matrix of the vertex resistances in G. In this paper, we obtain upper bounds on the minimal and maximal entries of the principal eigenvector of R(G) and RQ, respectively, and characterize the corresponding extremal graphs. In addition, a lower bound of the resistance (resp. resistance signless Laplacian) spectral radius of graphs with n vertices and independence number α is obtained, the corresponding extremal graph is also characterized.
- Subjects
LAPLACIAN matrices; MATHEMATICAL bounds; MATRICES (Mathematics); GRAPH connectivity
- Publication
Operators & Matrices, 2023, Vol 17, Issue 4, p1125
- ISSN
1846-3886
- Publication type
Article
- DOI
10.7153/oam-2023-17-74