On Kirchhoff index and number of spanning trees of linear pentagonal cylinder and Mobius chain graph
Md. Abdus Sahir, Sk. Md. Abu Nayeem
TL;DR
This paper derives explicit formulas for the Kirchhoff index, Wiener index, and the total number of spanning trees for linear pentagonal cylinder and Mobius chain graphs, providing new insights into their structural properties.
Contribution
It introduces closed-form formulas for key graph invariants and spanning tree counts of specific pentagonal chain graphs, advancing understanding of their combinatorial characteristics.
Findings
Closed-form formulas for Kirchhoff and Wiener indices
Explicit formulas for total spanning trees
Enhanced understanding of pentagonal chain graph properties
Abstract
In this paper, we derive closed-form formulas for Kirchhoff index and Wiener index of linear pentagonal cylinder graph and linear pentagonal Mobius chain graph. We also obtain explicit formulas for finding total number of spanning trees for both the graphs.
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Taxonomy
TopicsGraph theory and applications · Topological and Geometric Data Analysis · Complex Network Analysis Techniques