On the spectral radius of block graphs with prescribed independence number α

Conde, Cristian; Dratman, Ezequiel; Grippo, Luciano N.

doi:10.1016/j.laa.2020.02.003

Cited by 9 publications

(4 citation statements)

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“…Proposition 1 has also shown to be of help to find the unique graph with maximum spectral radius of block graphs with prescribed independence number [4].…”

Section: Tools For Finding the Maximummentioning

confidence: 98%

On the spectral radius of block graphs having all their blocks of the same size

Conde¹,

Dratman²,

Grippo³

2020

Preprint

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Let B(n, q) be the class of block graphs on n vertices having all its blocks of size q + 1 with q ≥ 2. In this article we prove that the maximum spectral radius ρ(G), among all graphs G ∈ B(n, q), is reached at a unique graph. We profit from this fact to present an tight upper bound for ρ(G). We also prove that if G has at most three pairwise adjacent cut vertices then the minimum ρ(G) is attained at a unique graph. Likewise, we present a lower bound for ρ(G) when G ∈ B(n, q).

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“…Proposition 1 has also shown to be of help to find the unique graph with maximum spectral radius of block graphs with prescribed independence number [4].…”

Section: Tools For Finding the Maximummentioning

confidence: 98%

On the spectral radius of block graphs having all their blocks of the same size

Conde¹,

Dratman²,

Grippo³

2020

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In this article, the authors obtained the graphs that maximize the spectral radius amongst graphs with a fixed number of vertices k in a given class of graphs. Later, several results in similar contexts has been published (for example see [6][7][8][9][10][12][13][14]19,20]). For a few more interesting results on spectral graph theory reader also may refer [16].…”

Section: Introductionmentioning

confidence: 99%

“…In [10], the authors found the graph that uniquely maximizes the spectral radius amongst the trees on fixed number of vertices k with a given independence number. Subsequently, characterizing extremal graphs with a given independence number were studied for various classes of graphs (for details see [6][7][8]20]). In particular, block graphs on fixed number of vertices k and with a given independence number has been studied in [6].…”

Section: Introductionmentioning

confidence: 99%

“…Subsequently, characterizing extremal graphs with a given independence number were studied for various classes of graphs (for details see [6][7][8]20]). In particular, block graphs on fixed number of vertices k and with a given independence number has been studied in [6]. Further, in [7], bi-block graphs (each of its block is a complete bipartite graph) has been studied, and later in [14] the results of bi-block graphs were extended for general bipartite graphs.…”

Section: Introductionmentioning

confidence: 99%

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