scholarly journals On the minimum number of spanning trees in cubic multigraphs

2020 ◽  
Vol 40 (1) ◽  
pp. 149
Author(s):  
Zbigniew R. Bogdanowicz
Keyword(s):  
Spanning Trees ◽  
Minimum Number ◽  
Number Of Spanning Trees

scholarly journals Two-cacti with minimum number of spanning trees

1994 ◽  
Vol 124 (1-3) ◽  
pp. 241-250
Author(s):  
Preben Dahl Vestergaard
Keyword(s):  
Spanning Trees ◽  
Minimum Number ◽  
Number Of Spanning Trees

scholarly journals Properties of Commuting Graphs over Semidihedral Groups

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 103
Author(s):  
Tao Cheng ◽  
Matthias Dehmer ◽  
Frank Emmert-Streib ◽  
Yongtao Li ◽  
Weijun Liu
Keyword(s):  
Spanning Trees ◽  
Laplacian Spectrum ◽  
Vertex Connectivity ◽  
Laplacian Energy ◽  
Number Of Spanning Trees

This paper considers commuting graphs over the semidihedral group SD8n. We compute their eigenvalues and obtain that these commuting graphs are not hyperenergetic for odd n≥15 or even n≥2. We further compute the Laplacian spectrum, the Laplacian energy and the number of spanning trees of the commuting graphs over SD8n. We also discuss vertex connectivity, planarity, and minimum disconnecting sets of these graphs and prove that these commuting graphs are not Hamiltonian.

scholarly journals On the characterization of graphs with maximum number of spanning trees

1998 ◽  
Vol 179 (1-3) ◽  
pp. 155-166 ◽  
Author(s):  
L. Petingi ◽  
F. Boesch ◽  
C. Suffel
Keyword(s):  
Spanning Trees ◽  
Number Of Spanning Trees

Determinant of links, spanning trees, and a theorem of Shank

2016 ◽  
Vol 25 (09) ◽  
pp. 1641005
Author(s):  
Jun Ge ◽  
Lianzhu Zhang
Keyword(s):  
Spanning Trees ◽  
Elementary Proof ◽  
Number Of Spanning Trees

In this note, we first give an alternative elementary proof of the relation between the determinant of a link and the spanning trees of the corresponding Tait graph. Then, we use this relation to give an extremely short, knot theoretical proof of a theorem due to Shank stating that a link has component number one if and only if the number of spanning trees of its Tait graph is odd.

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