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

Abstract

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.

Keywords

• number of spanning trees
• matrix tree theorem
• recurrence relation