On the number of spanning trees in directed circulant graphs

Networks ◽  
10.1002/net.2 ◽  
2001 ◽  
Vol 37 (3) ◽  
pp. 129-133 ◽  
Author(s):  
Zbigniew Lonc ◽  
Krzysztof Parol ◽  
Jacek M. Wojciechowski
Keyword(s):  
Spanning Trees ◽  
Circulant Graphs ◽  
Number Of Spanning Trees

scholarly journals On Rationality of Generating Function for the Number of Spanning Trees in Circulant Graphs

2020 ◽  
Vol 27 (01) ◽  
pp. 87-94
Author(s):  
A.D. Mednykh ◽  
I.A. Mednykh
Keyword(s):  
Rational Function ◽  
Generating Function ◽  
Spanning Trees ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Integer Coefficients ◽  
Number Formula ◽  
Number Of Spanning Trees

Let [Formula: see text] be the generating function for the number [Formula: see text] of spanning trees in the circulant graph Cn(s1, s2, …, sk). We show that F(x) is a rational function with integer coefficients satisfying the property F(x) = F(1/x). A similar result is also true for the circulant graphs C2n(s1, s2, …, sk, n) of odd valency. We illustrate the obtained results by a series of examples.

scholarly journals Further analysis of the number of spanning trees in circulant graphs

2006 ◽  
Vol 306 (22) ◽  
pp. 2817-2827 ◽  
Author(s):  
Talip Atajan ◽  
Xuerong Yong ◽  
Hiroshi Inaba
Keyword(s):  
Spanning Trees ◽  
Circulant Graphs ◽  
Number Of Spanning Trees

scholarly journals A FORMULA FOR THE NUMBER OF SPANNING TREES IN CIRCULANT GRAPHS WITH NONFIXED GENERATORS AND DISCRETE TORI

2015 ◽  
Vol 92 (3) ◽  
pp. 365-373 ◽  
Author(s):  
JUSTINE LOUIS
Keyword(s):  
Spanning Tree ◽  
Spanning Trees ◽  
Closed Formula ◽  
Circulant Graphs ◽  
The Matrix ◽  
Number Of Spanning Trees

We consider the number of spanning trees in circulant graphs of ${\it\beta}n$ vertices with generators depending linearly on $n$. The matrix tree theorem gives a closed formula of ${\it\beta}n$ factors, while we derive a formula of ${\it\beta}-1$ factors. We also derive a formula for the number of spanning trees in discrete tori. Finally, we compare the spanning tree entropy of circulant graphs with fixed and nonfixed generators.

scholarly journals The number of spanning trees in circulant graphs

2000 ◽  
Vol 223 (1-3) ◽  
pp. 337-350 ◽  
Author(s):  
Yuanping Zhang ◽  
Xuerong Yong ◽  
Mordecai J. Golin
Keyword(s):  
Spanning Trees ◽  
Circulant Graphs ◽  
Number Of Spanning Trees

scholarly journals The number of spanning trees in odd valent circulant graphs

2004 ◽  
Vol 282 (1-3) ◽  
pp. 69-79 ◽  
Author(s):  
Xiebin Chen ◽  
Qiuying Lin ◽  
Fuji Zhang
Keyword(s):  
Spanning Trees ◽  
Circulant Graphs ◽  
Number Of Spanning Trees
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