On the Number of Spanning Trees in Augmented Triangular Prism Graphs

In computer science and graph theory, prism and antiprism graphs are crucial for network modeling, optimization, and network connectivity comprehension. Applications such as social network analysis, fault-tolerant circuit design, and parallel and distributed computing all make use of them. Their structured nature makes them important, since it offers a framework for researching intricate characteristics, including resilient design, communication patterns, and network efficiency. This work uses the electrically equivalent transformations technique to compute the explicit formulas for the number of spanning trees of three novel families of graphs that have been produced using triangular prisms with their distinctive iteration feature. Additionally, the relationship between these graphs’ average degree and entropy is examined and contrasted with the entropy of additional graphs that share the same average degree as these previously studied graphs.