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    On plane graphs with link component number equal to the nullity

    Lin, Y. and Noble, Steven and Jin, X. and Cheng, W. (2012) On plane graphs with link component number equal to the nullity. Discrete Applied Mathematics 160 (9), pp. 1369-1375. ISSN 0166-218X.

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    Abstract

    In this paper, we study connected plane graphs with link component number equal to the nullity and call them near-extremal graphs. We first study near-extremal graphs with minimum degree at least 3 and prove that a connected plane graph with minimum degree at least 3 is a near-extremal graph if and only if is isomorphic to , the complete graph with 4 vertices. The result is obtained by studying general graphs using the knowledge of bicycle space and the Tutte polynomial. Then a simple algorithm is given to judge whether a connected plane graph is a near-extremal graph or not. Finally we study the construction of near-extremal graphs and prove that all near-extremal graphs can be constructed from a loop and by two graph operations.

    Metadata

    Item Type: Article
    School: School of Business, Economics & Informatics > Economics, Mathematics and Statistics
    Depositing User: Administrator
    Date Deposited: 06 Jan 2023 14:19
    Last Modified: 06 Jan 2023 14:23
    URI: https://eprints.bbk.ac.uk/id/eprint/50372

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