Complexity trees of the sequence of some nonahedral graphs generated by triangle

S N Daoud; Wedad Saleh

doi:10.1016/j.heliyon.2020.e04786

Complexity trees of the sequence of some nonahedral graphs generated by triangle

Heliyon. 2020 Sep 14;6(9):e04786. doi: 10.1016/j.heliyon.2020.e04786. eCollection 2020 Sep.

Authors

S N Daoud^{1

2}, Wedad Saleh¹

Affiliations

¹ Department of Mathematics, Faculty of Science, Taibah University, Al-Madinah 41411, Saudi Arabia.
² Department of Mathematics and Computer Science, Faculty of Science, Menoufia University, Shebin El Kom 32511, Egypt.

Abstract

Calculating the number of spanning trees of a graph is one of the widely studied graph problems since the Pioneer Gustav Kirchhoff (1847). In this work, using knowledge of difference equations we drive the explicit formulas for the number of spanning trees in the sequence of some Nonahedral (nine faced polyhedral) graphs generated by triangle using electrically equivalent transformations and rules of the weighted generating function. Finally, we evaluate the entropy of graphs in this manuscript with different studied graphs with an average degree being 4, 5 and 6.

Keywords: Electrically equivalent transformations; Entropy; Mathematics; Number of spanning trees.