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DC Field | Value | Language |
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dc.contributor.author | Oboudi, M.R. | - |
dc.date.accessioned | 2019-12-18T10:57:01Z | - |
dc.date.available | 2019-12-18T10:57:01Z | - |
dc.date.issued | 2017 | - |
dc.identifier.uri | http://hdl.handle.net/123456789/4564 | - |
dc.description | Oboudi M.R. On the difference between the spectral radius and the maximum degree of graphs / M.R.Oboudi // Algebra and Discrete Mathematics. - 2017. - Vol. 24. - Number 2. - Рp. 302-307 | uk_UA |
dc.description.abstract | Let G be a graph with the eigenvalues λ1(G) >· · · > λn(G). The largest eigenvalue of G, λ1(G), is called the spectral radius of G. Let β(G) = ∆(G) − λ1(G), where ∆(G) is the maximum degree of vertices of G. It is known that if G is a connected graph, then β(G) > 0 and the equality holds if and only if G is regular. In this paper we study the maximum value and the minimum value of β(G) among all non-regular connected graphs. In particular we show that for every tree T with n > 3 vertices, n − 1 − √ n − 1 > β(T) > 4 sin2 (π2n+2 ). Moreover, we prove that in the right side the equality holds if and only if T ∼= Pn and in the other side the equality holds if and only if T ∼= Sn, where Pn and Sn are the path and the star on n vertices, respectively. | uk_UA |
dc.language.iso | en | uk_UA |
dc.publisher | ДЗ "ЛНУ імені Тараса Шевченка" | uk_UA |
dc.relation.ispartofseries | математичні науки; | - |
dc.subject | tree | uk_UA |
dc.subject | eigenvalues of graphs | uk_UA |
dc.subject | spectral radius of graphs | uk_UA |
dc.subject | maximum degree | uk_UA |
dc.title | On the difference between the spectral radius and the maximum degree of graphs∗ | uk_UA |
dc.type | Article | uk_UA |
Appears in Collections: | Algebra and Discrete Mathematics. - № 2 (24). - 2017 |
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File | Description | Size | Format | |
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303-2040-2-PB.pdf | 287.36 kB | Adobe PDF | View/Open |
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