The deletion-contraction method for counting the number of spanning trees of graphs

2019

Complexity

Self Cite

In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. 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 transformations and rules of weighted generating function. Finally, we compare the entropy of our graphs with other studied graphs with average degree being 4, 5, and 6.

Section: Introductionmentioning

confidence: 99%

Number of Spanning Trees in the Sequence of Some Graphs

Liu

2019

Complexity

Self Cite

“…Another class of graphs for which an explicit formula has been derived is based on a prism [13,14]. Many works have conceived techniques to derive the number of spanning tree of a graph, which can be found at [15][16][17][18][19][20][21][22][23]. Now we introduce following Lemma which describes a way to calculate the number of spanning trees by an extension of Kirchhoff formula.…”

Section: Introductionmentioning

confidence: 99%

Number of spanning trees of some families of graphs generated by a triangle

Journal of Taibah University for Science

2019

Self Cite

In mathematics, one always tries to get new structures from given ones. This also applies to the realm of graphs, where one can generate many new graphs from a given set of graphs. In this paper, we derive simple formulas of spanning trees of some families of graphs generated by triangle using linear algebra and the knowledge of difference equations. Finally, we compare the entropy of our graphs with other studied graphs with the average degree being 4 and 6. ARTICLE HISTORY

“…One of the favorite methods of calculating the complexity is the contraction-deletion theorem. For any graph G, the complexity τ(G) of G is equal to τ(G) = τ(G − e) + τ(G/e), where e is any edge of G, and where G − e is the deletion of e from G, and G/e is the contraction of e in G. This gives a recursive method to calculate the complexity of a graph [13,14].…”

Section: Introductionmentioning

confidence: 99%

The Complexity of Some Classes of Pyramid Graphs Created from a Gear Graph

Liu

2018

Symmetry

The methods of measuring the complexity (spanning trees) in a finite graph, a problem related to various areas of mathematics and physics, have been inspected by many mathematicians and physicists. In this work, we defined some classes of pyramid graphs created by a gear graph then we developed the Kirchhoff's matrix tree theorem method to produce explicit formulas for the complexity of these graphs, using linear algebra, matrix analysis techniques, and employing knowledge of Chebyshev polynomials. Finally, we gave some numerical results for the number of spanning trees of the studied graphs.