التفاصيل البيبلوغرافية
| العنوان: |
On spectral spread of generalized distance matrix of a graph. |
| المؤلفون: |
Pirzada, S., Ganie, H. A., Alhevaz, A., Baghipur, M. |
| المصدر: |
Linear & Multilinear Algebra; Oct2022, Vol. 70 Issue 15, p2819-2835, 17p |
| مصطلحات موضوعية: |
LAPLACIAN matrices, CHARTS, diagrams, etc., BIPARTITE graphs, GRAPH connectivity, SPECTRAL theory, MATRICES (Mathematics), EIGENVALUES |
| مستخلص: |
For a simple connected graph G, let D (G) , T r (G) , D L (G) and D Q (G) , respectively, are the distance matrix, the diagonal matrix of the vertex transmissions, distance Laplacian matrix and the distance signless Laplacian matrix. The generalized distance matrix D α (G) of G is the convex linear combinations of T r (G) and D (G) and is defined as D α (G) = α T r (G) + (1 − α) D (G) , for 0 ≤ α ≤ 1. As D 0 (G) = D (G) , 2 D 1 2 (G) = D Q (G) , D 1 (G) = T r (G) and D α (G) − D β (G) = (α − β) D L (G) , this matrix reduces to merging the distance spectral and distance signless Laplacian spectral theories. Let ∂ 1 (G) ≥ ∂ 2 (G) ≥ ⋯ ≥ ∂ n (G) be the eigenvalues of D α (G) and let S D α (G) = ∂ 1 (G) − ∂ n (G) be the generalized distance spectral spread of the graph G. In this paper, we obtain bounds for the generalized distance spectral spread S D α (G). We also obtain a relation between the generalized distance spectral spread S D α (G) and the distance spectral spread S D (G). Further, we obtain lower bounds for S D α (G) of bipartite graphs involving different graph parameters and we characterize the extremal graphs for some cases. We also obtain lower bounds for S D α (G) in terms of clique number and independence number of the graph G and characterize the extremal graphs for some cases. [ABSTRACT FROM AUTHOR] |
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| قاعدة البيانات: |
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