On unimodular tricyclic graphs with a unique perfect matching

Articles in Press

Document Type : Original paper

Authors

1 Department of Mathematics, Salbari College, Salbari, Baksa, BTC, Assam-781318, India

2 Department of Mathematical Sciences, Tezpur University, Napaam, Sonitpur, Assam-784028, India

Abstract

A graph is called unimodular if the determinant of its adjacency matrix is $\pm1$. Akbari and Kirkland [\textit{Linear Algebra and its Applications}, 421(1):3--15, 2007.] proved that a unicyclic graph is unimodular precisely when it has a unique perfect matching. However, a bicyclic or tricyclic graph with a unique perfect matching need not be unimodular. Recently, Basumatary and Sarma [\textit{Discrete Applied Mathematics}, 346:49-61, 2024.] characterized those bicyclic graphs with a unique perfect matching that are unimodular. In this article, we identify which tricyclic graphs with a unique perfect matching possess the unimodularity property. Our results provide a complete characterization of such graphs.

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References

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Communications in Combinatorics and Optimization

Articles in Press, Accepted Manuscript
Available Online from 31 May 2026

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