The connectivity and Hamiltonian properties of second-order circuit graphs of wheel cycle matroids
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Published:2021-11-06
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ISSN:1793-8309
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Container-title:Discrete Mathematics, Algorithms and Applications
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language:en
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Short-container-title:Discrete Math. Algorithm. Appl.
Author:
Deng Zijian1,
Liu Bin1,
Huo Bofeng1,
Deng Bo1
Affiliation:
1. School of Mathematics and Statistics, Qinghai Normal University, Xining, Qinghai 810008, P. R. China
Abstract
Let [Formula: see text] be the [Formula: see text]th-order circuit graph of a simple connected matroid M. The first-order circuit graph is also called a circuit graph. There are lots of results about connectivity and Hamiltonian properties of circuit graph of matroid, while there are few related results on the second-order circuit graph of a matroid. This paper mainly focuses on the connectivity and Hamiltonian properties of the second-order circuit graphs of the cycle matroid of wheels. It determines the minimum degree and connectivity of these graphs, and proves that the second-order circuit graph of the cycle matroid of a wheel is uniformly Hamiltonian.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Discrete Mathematics and Combinatorics