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

1995
*
Random structures & algorithms (Print)
*

Alon's [l] idea is slightly refined to prove that for each connected

doi:10.1002/rsa.3240060214
fatcat:dq7pzwcuvjfu5nzqtpvde4cohq
*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. ...##
###
Number of Spanning Trees in the Sequence of Some Graphs

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 ...

##
###
Degree sums and dense spanning trees

2017
*
PLoS ONE
*

Finding dense

doi:10.1371/journal.pone.0184912
pmid:28926585
pmcid:PMC5605090
fatcat:a4cy5k6zkbexbilg3btqgtjwei
*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. ...##
###
An Approach of Degree Constraint MST Algorithm

2013
*
International Journal of Information Technology and Computer Science
*

Here we recommend a new algorith m based on

doi:10.5815/ijitcs.2013.09.08
fatcat:kfbdjx3zznds5plarqaezs6nkq
*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. ...##
###
Complexity of computation of a spanning tree enumeration algorithm

1984
*
IEEE Transactions on Circuits and Systems
*

These heuristics result

doi:10.1109/tcs.1984.1085435
fatcat:lnk24tis6relzhbeaihsfyphli
*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 ...##
###
Measuring the effectiveness of the s-metric to produce better network models

2008
*
2008 Winter Simulation Conference
*

random models

doi:10.1109/wsc.2008.4736169
dblp:conf/wsc/BeichlC08
fatcat:ubpnlmrfcbgy3fngvx67435wci
*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. ...##
###
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

2010
*
Zenodo
*

Path-Growing

doi:10.5281/zenodo.1332106
fatcat:cbyjsmqsnvhi5l3ieqq6r2bpby
*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 . ...##
###
A network-flow technique for finding low-weight bounded-degree spanning trees
[chapter]

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 ...

##
###
Globally Optimal Dense and Sparse Spanning Trees, and their Applications

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. ...

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

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 ...

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

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. ...

##
###
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

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. ...

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