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

CONSTRUCTING MULTIPLE INDEPENDENT SPANNING TREES ON RECURSIVE CIRCULANT GRAPHS G(2m, 2)

2010 ◽  
Vol 21 (01) ◽  
pp. 73-90 ◽  
Author(s):  
JINN-SHYONG YANG ◽  
JOU-MING CHANG ◽  
SHYUE-MING TANG ◽  
YUE-LI WANG
Keyword(s):  
Interconnection Networks ◽  
Spanning Trees ◽  
Fault Tolerant ◽  
Network Communication ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Recursive Structure ◽  
Computing Systems ◽  
Independent Spanning Trees ◽  
Optimal Construction

A recursive circulant graph G(N,d) has N = cdm vertices labeled from 0 to N - 1, where d ⩾ 2, m ⩾ 1, and 1 ⩽ c < d, and two vertices x,y ∈ G(N,d) are adjacent if and only if there is an integer k with 0 ⩽ k ⩽ ⌈ log d N⌉ - 1 such that x ± dk ≡ y ( mod N). With the aid of recursive structure, such class of graphs has many attractive features and was considered as a topology of interconnection networks for computing systems. The design of multiple independent spanning trees (ISTs) has many applications in network communication. For instance, it is useful for fault-tolerant broadcasting and secure message distribution. In the previous work of Yang et al. (2009), we provided a constructing scheme to build k ISTs on G(cdm,d) with d ⩾ 3, where k is the connectivity of G(cdm,d). However, the proposed constructing rules cannot be applied to the case of d = 2. For the integrity of solving the IST problem on recursive circulant graphs, this paper deals with the case of G(2m,2) using a set of different constructing rules. Especially, we show that the heights of ISTs for G(2m,2) are lower than the known optimal construction of hypercubes with the same number of vertices.

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 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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