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The number of spanning trees in graphs with a given degree sequence

A. V. Kostochka
1995 Random structures & algorithms (Print)  
Alon's [l] idea is slightly refined to prove that for each connected graph G with degree sequence 1 < k = d , 5 d , 5 . . .5 d, the number C ( C ) of spanning trees of G satisfies the inequality d(G)k-n  ...  INTRODUCTION All graphs considered here are simple connected graphs. For a graph G on n vertices let C ( G ) denote the number of spanning trees of G and c(G) = (C(G))"".  ...  H) the number of vertices of degree 3 in H and f(H) = 23(m(H)+2)/4. Let us count C ( G ) for several G.  ... 
doi:10.1002/rsa.3240060214 fatcat:dq7pzwcuvjfu5nzqtpvde4cohq

Number of Spanning Trees in the Sequence of Some Graphs

Jia-Bao Liu, S. N. Daoud
2019 Complexity  
In this work, using knowledge of difference equations, we drive the explicit formulas for the number of spanning trees in the sequence of some graphs generated by a triangle by electrically equivalent  ...  Finally, we compare the entropy of our graphs with other studied graphs with average degree being 4, 5, and 6.  ...  Acknowledgments The work was partially supported by the National Natural Science Foundation of China under the grant No. 11601006, and China Postdoctoral Science Foundation under  ... 
doi:10.1155/2019/4271783 fatcat:i5p634crjfhlxgw6hsblzsmawy

Degree sums and dense spanning trees

Tao Li, Yingqi Gao, Qiankun Dong, Hua Wang, Jianhua Tu
2017 PLoS ONE  
Finding dense spanning trees (DST) in unweighted graphs is a variation of the well studied minimum spanning tree problem (MST).  ...  Our work provide some insights on the role of various degree sums in forming dense spanning trees and hopefully lay the foundation for finding fast algorithms or heuristics for related problems.  ...  Degree sequence and the greedy tree In the study of dense trees, trees with a given degree sequence (non-increasing sequence of vertex degrees) are often considered.  ... 
doi:10.1371/journal.pone.0184912 pmid:28926585 pmcid:PMC5605090 fatcat:a4cy5k6zkbexbilg3btqgtjwei

An Approach of Degree Constraint MST Algorithm

Sanjay Kumar Pal, Samar Sen Sarma
2013 International Journal of Information Technology and Computer Science  
Here we recommend a new algorith m based on the average degree sequence factor of the nodes in the graph.  ...  This paper is approaching a new technique of creating Minimal Spanning Trees based on degree constraints of a simp le symmetric and connected graph G.  ...  Hence there exist graphs of order n with degree sequence D.  ... 
doi:10.5815/ijitcs.2013.09.08 fatcat:kfbdjx3zznds5plarqaezs6nkq

Complexity of computation of a spanning tree enumeration algorithm

R. Jayakumar, K. Thulasiraman, M. Swamy
1984 IEEE Transactions on Circuits and Systems  
These heuristics result in a considerable reduction in the number of spanning non-tree subgraphs generated.  ...  This algorithm starts with a known initial spanning tree of G, and generates all the other spanning trees along with certain spanning non-tree subgraphs of G.  ...  ACKNOWLEDGMENT The authors thank the reviewers for their suggestions which have resulted in considerable improvement in the presentation of the paper. PI PI  ... 
doi:10.1109/tcs.1984.1085435 fatcat:lnk24tis6relzhbeaihsfyphli

Measuring the effectiveness of the s-metric to produce better network models

Isabel Beichl, Brian Cloteaux
2008 2008 Winter Simulation Conference  
random models with identical degree sequences and similar s values.  ...  In order to better distinguish between these networks, the metric s was introduced to measure how interconnected the hub nodes are in a network.  ...  This work is a contribution of NIST, an agency of the US government, and is not subject to US copyright.  ... 
doi:10.1109/wsc.2008.4736169 dblp:conf/wsc/BeichlC08 fatcat:ubpnlmrfcbgy3fngvx67435wci

Page 4661 of Mathematical Reviews Vol. , Issue 80M [page]

1980 Mathematical Reviews  
Ramachandra Rao, A. 80m:05058 The clique number of a graph with a given degree sequence. Proceedings of the Symposium on Graph Theory (Indian Statist.  ...  From the summary: “We give a Havel-Hakimi-type procedure to determine the maximum clique number of a graph with a given degree sequence.  ... 

Page 5473 of Mathematical Reviews Vol. , Issue 2002H [page]

2002 Mathematical Reviews  
vertices, have out-degree 2 in the tree.” 2002h:05049 05C05 Polat, Norbert Multi-faithful spanning trees of infinite graphs.  ...  Beineke (1-INPFW; Fort Wayne, IN) 2002h:05046 05C05 Kaneko, Atsushi Spanning trees with constraints on the leaf degree.  ... 

Spanning Tree Transformation Of Connected Graphs Into Single-Row Networks

S.L. Loh, S. Salleh, N.H. Sarmin
2010 Zenodo  
Path-Growing Tree-Forming algorithm applied with Vertex-Prioritized is contained in the model to produce the spanning tree from the connected graph.  ...  A spanning tree of a connected graph is a tree which consists the set of vertices and some or perhaps all of the edges from the connected graph.  ...  Fig. 2 A connected graph, 9 G G of node ( max D ) in the spanning tree n SP together with the total number of nodes with degree of max D that exist in the n SP .  ... 
doi:10.5281/zenodo.1332106 fatcat:cbyjsmqsnvhi5l3ieqq6r2bpby

A network-flow technique for finding low-weight bounded-degree spanning trees [chapter]

Sándor P. Fekete, Samir Khuller, Monika Klemmstein, Balaji Raghavachari, Neal Young
1996 Lecture Notes in Computer Science  
Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, the problem of computing a low-weight spanning tree such that the degree of each vertex is at most  ...  In particular, modifying a given spanning tree T using adoptions to meet the degree constraints is considered.  ...  Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, the problem of computing a low-weight spanning tree such that the degree of each vertex is at most  ... 
doi:10.1007/3-540-61310-2_9 fatcat:mdno4d46ifa6jalgoqnjwbwytm

Globally Optimal Dense and Sparse Spanning Trees, and their Applications

Mustafa Ozen, Goran Lesaja, Hua Wang
2020 Statistics, Optimization and Information Computing  
spanning trees of the graph under consideration.  ...  Recently, a novel notion of dense ( sparse ) tree, and in particular spanning tree (DST and SST respectively), is introduced as the structure that have a large (small) number of subtrees, or small (large  ...  Acknowledgment The authors declare that no conflict of interests exist.  ... 
doi:10.19139/soic-2310-5070-855 fatcat:bz27zce6x5bvzlqtirxcrmpxjy

A Network-Flow Technique for Finding Low-Weight Bounded-Degree Spanning Trees

Sándor P Fekete, Samir Khuller, Monika Klemmstein, Balaji Raghavachari, Neal Young
1997 Journal of Algorithms  
Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, compute a low-weight spanning tree such that the degree of each vertex is at most its specified bound  ...  The paper also describes a Euclidean graph whose minimum TSP costs twice the MST, disproving a conjecture made in "Low-Degree Spanning Trees of Small Weight" (1996).  ...  Given a graph with edge weights satisfying the triangle inequality, and a degree bound for each vertex, the problem of computing a low-weight spanning tree such that the degree of each vertex is at most  ... 
doi:10.1006/jagm.1997.0862 fatcat:5wp37vrggrcyzcybwqek4yla6m

Globally optimal dense and sparse spanning trees, and their applications [article]

Mustafa Ozen, Goran Lesaja, Hua Wang
2020 arXiv   pre-print
spanning trees of the graph under consideration.  ...  Recently, a novel notion of "dense" ("sparse") tree, and in particular spanning tree (DST and SST respectively), is introduced as the structure that have a large (small) number of subtrees, or small (large  ...  Acknowledgement The authors declare that no conflict of interests exist.  ... 
arXiv:2001.06958v1 fatcat:ib5we3juzbcb7c4h6yuupjx4ai

Page 3027 of Mathematical Reviews Vol. , Issue 2002E [page]

2002 Mathematical Reviews  
The main theorem states that in a connected graph G in which no two vertices of degree 2 are adjacent there exists a spanning tree in which the number of pendant vertices is more than one fifth of the  ...  These entities are then used to prepro- cess a given graph with interval data prior to the solution of the robust spanning tree problem.  ... 

Minimum edge ranking spanning trees of split graphs

Kazuhisa Makino, Yushi Uno, Toshihide Ibaraki
2006 Discrete Applied Mathematics  
Given a graph G, the minimum edge ranking spanning tree problem (MERST) is to find a spanning tree of G whose edge ranking is minimum. However, this problem is known to be NP-hard for general graphs.  ...  In this paper, we show that the problem MERST has a polynomial time algorithm for split graphs, which have useful applications in practice.  ...  Acknowledgments This research was partially supported by the Scientific Grant-in-Aid from Ministry of Education, Science, Sports, Culture and Technology of Japan.  ... 
doi:10.1016/j.dam.2006.04.018 fatcat:f6tlai5tqnb2xixrv6q2tgowcq
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