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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 |
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