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Anti-forcing spectra of perfect matchings of graphs

Author

Listed:
  • Kai Deng

    (Lanzhou University
    Beifang University of Nationalities)

  • Heping Zhang

    (Lanzhou University)

Abstract

Let M be a perfect matching of a graph G. The smallest number of edges whose removal to make M as the unique perfect matching in the resulting subgraph is called the anti-forcing number of M. The anti-forcing spectrum of G is the set of anti-forcing numbers of all perfect matchings in G, denoted by $$\hbox {Spec}_{af}(G)$$ Spec a f ( G ) . In this paper, we show that any finite set of positive integers can be the anti-forcing spectrum of a graph. We present two classes of hexagonal systems whose anti-forcing spectra are integer intervals. Finally, we show that determining the anti-forcing number of a perfect matching of a bipartite graph with maximum degree four is a NP-complete problem.

Suggested Citation

  • Kai Deng & Heping Zhang, 2017. "Anti-forcing spectra of perfect matchings of graphs," Journal of Combinatorial Optimization, Springer, vol. 33(2), pages 660-680, February.
    • Handle: RePEc:spr:jcomop:v:33:y:2017:i:2:d:10.1007_s10878-015-9986-3
    DOI: 10.1007/s10878-015-9986-3
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    Cited by:

    1. Shi, Lingjuan & Zhang, Heping & Zhao, Lifang, 2022. "The anti-forcing spectra of (4,6)-fullerenes," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Yaxian Zhang & Bo Zhang & Heping Zhang, 2022. "Anti-Forcing Spectra of Convex Hexagonal Systems," Mathematics, MDPI, vol. 10(19), pages 1-21, September.

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