Bu öğeden alıntı yapmak, öğeye bağlanmak için bu tanımlayıcıyı kullanınız: http://hdl.handle.net/11452/32849
Başlık: The number of spanning trees of a graph
Yazarlar: Das, Kinkar Chandra
Çevik, Ahmet Sinan
Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Anabilim Dalı.
0000-0002-0700-5774
0000-0003-2576-160X
Cangül, İsmail Naci
J-3505-2017
57189022403
Anahtar kelimeler: Mathematics
Graph
Spanning trees
Independence number
Clique number
First Zagreb index
Molecular-orbitals
Zagreb indexes
Yayın Tarihi: Ağu-2013
Yayıncı: Springer
Atıf: Das, K. C. vd. (2013). “The number of spanning trees of a graph”. Journal of Inequalities and Applications, 2013.
Özet: Let G be a simple connected graph of order n, m edges, maximum degree Delta(1) and minimum degree delta. Li et al. (Appl. Math. Lett. 23: 286-290, 2010) gave an upper bound on number of spanning trees of a graph in terms of n, m, Delta(1) and delta: t(G) <= delta (2m-Delta(1)-delta-1/n-3)(n-3). The equality holds if and only if G congruent to K-1,K-n-1, G congruent to K-n, G congruent to K-1 boolean OR (K-1 boolean OR Kn-2) or G congruent to K-n - e, where e is any edge of K-n. Unfortunately, this upper bound is erroneous. In particular, we show that this upper bound is not true for complete graph K-n. In this paper we obtain some upper bounds on the number of spanning trees of graph G in terms of its structural parameters such as the number of vertices (n), the number of edges (m), maximum degree (Delta(1)), second maximum degree (Delta(2)), minimum degree (delta), independence number (alpha), clique number (omega). Moreover, we give the Nordhaus-Gaddum-type result for number of spanning trees.
URI: https://doi.org/10.1186/1029-242X-2013-395
https://doi.org/10.1186/1029-242X-2013-395
http://hdl.handle.net/11452/32849
ISSN: 1029-242X
Koleksiyonlarda Görünür:Scopus
Web of Science

Bu öğenin dosyaları:
Dosya Açıklama BoyutBiçim 
Cangül_vd_2013.pdf325.18 kBAdobe PDFKüçük resim
Göster/Aç


Bu öğe kapsamında lisanslı Creative Commons License Creative Commons