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- Title
Sharp bounds for spectral radius of Dα-matrix of graphs.
- Authors
Ganie, Hilal A.
- Abstract
For a simple connected graph G , the generalized distance matrix D α (G) is defined as D α (G) = α Tr (G) + (1 − α) D (G) , 0 ≤ α ≤ 1 , where Tr (G) and D (G) are, respectively, the diagonal matrix of vertex transmission degrees and the distance matrix of G. In this paper, we will study the spectral radius of the generalized distance matrix D α (G) of a connected graph G. We obtain some upper and lower bounds for the generalized distance spectral radius in terms of various parameters, like the vertex transmission degrees, the average transmission 2-degrees, etc., associated with the structure of the graph. We characterize the extremal graphs attaining these bounds. Further, we show that our bounds improve some previously known bounds existing in the literature.
- Subjects
MATHEMATICAL bounds; GRAPH connectivity; LAPLACIAN matrices; RADIUS (Geometry)
- Publication
Discrete Mathematics, Algorithms & Applications, 2023, Vol 15, Issue 8, p1
- ISSN
1793-8309
- Publication type
Article
- DOI
10.1142/S179383092250166X