On the two largest eigenvalues of trees

Hofmeister, M.

doi:10.1016/s0024-3795(97)80004-3

Cited by 27 publications

(4 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Then refining this upper bound on ϑ 1 (T ) at each step, we have obtained that S n , S 2 n , S 3 n , S 4 n are the trees with first four values of ϑ 1 (T ) in T n . As expected, we notice that ordering of trees according the ABC spectral radius is different than the ordering of trees according the spectral radius as given in Hofmeister [15].…”

Section: Resultssupporting

confidence: 62%

See 1 more Smart Citation

Bounds on the ABC spectral radius of a tree

Barik

Rani

2020

EJGTA

View full text Add to dashboard Cite

Let G be a simple connected graph with vertex set {1, 2,. .. , n} and d i denote the degree of vertex i in G. The ABC matrix of G, recently introduced by Estrada, is the square matrix whose ijth entry is d i +d j −2 d i d j ; if i and j are adjacent, and zero; otherwise. The entries in ABC matrix represent the probability of visiting a nearest neighbor edge from one side or the other of a given edge in a graph. In this article, we provide bounds on ABC spectral radius of G in terms of the number of vertices in G. The trees with maximum and minimum ABC spectral radius are characterized. Also, in the class of trees on n vertices, we obtain the trees having first four values of ABC spectral radius and subsequently derive a better upper bound.

show abstract

Section: Resultssupporting

confidence: 62%

“…Let us recall the following classical result concerning bounds on the spectral radius of trees. Hofmeister [15] has refined the above result and obtained the following.…”

Section: Resultsmentioning

confidence: 82%

Bounds on the ABC spectral radius of a tree

Barik

Rani

2020

EJGTA

View full text Add to dashboard Cite

show abstract

“…Let F n (n ≥ 5) be the tree obtained by coalescing the center of the star S n−4 and the center of the path P 5 . Ordering the trees on n vertices according to their spectral radii was well studied in [10], [4] and [12]. We outline parts of the work in [10] as follows.…”

Section: Moreover the Weighted Incidence Matrix B Is Called Consistementioning

confidence: 99%

“…Theorem 14 [10] Let T be a tree on n vertices (n ≥ 5) and T / ∈ {S n , S(1, n − 3), S(2, n − 4), F n }. Then we have ρ(S n ) > ρ(S(1, n − 3)) > ρ(S(2, n − 4)) > ρ(F n ) > ρ(T ).…”

Section: Moreover the Weighted Incidence Matrix B Is Called Consistementioning

confidence: 99%

Ordering uniform supertrees by their spectral radii

Yuan

Zhang

2017

Front. Math. China

View full text Add to dashboard Cite

A connected and acyclic hypergraph is called a supertree. In this paper we mainly focus on the spectral radii of uniform supertrees. Li, Shao and Qi determined the first two k-uniform supertrees with large spectral radii among all the k-uniform supertrees on n vertices [H. Li, J. Shao, L. Qi, The extremal spectral radii of k-uniform supertrees, arXiv:1405.7257v1, May 2014]. By applying the operation of moving edges on hypergraphs and using the weighted incidence matrix method we extend the above order to the fourth k-uniform supertree.

show abstract