The Problom of Forcing Number of Perfect Matching

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Ghanbari, Babak | 2019

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Type of Document: M.Sc. Thesis
Language: Farsi
Document No: 52571 (02)
University: Sharif University of Technology
Department: Mathematical Sciences
Advisor(s): Mahmoodian, Ebadollah; Ebrahimi Borogerdi, Javad
Abstract:
The notions of forcing edge and the forcing number of a perfect matching first appeared in 1991 by Harary, Klein and Živković. The root of these concepts can be traced to the works by Randić and Klein in 1985-1987, where the forcing number was introduced under the name of “innate degree of freedom” of a Kekulé structure, which plays an important role in the resonance theory in chemistry. Over the past three decades, more research has been done on the forcing set of perfect matchings. Here, we introduce bounds on the forcing number of perfect matching of some graphs that have already been known. Then, we extend the concept of forcing to fractional perfect matching and we introduce fractional forcing of the graphs. Finally, we use our results to conclude a new upper bound for the maximum forcing number of hypercube
Keywords:
Forcing Sets ; Forcing Domination Number ; Antiforcing Set ; Forcing Fractional Matching ; Antiforcing Number ; Perfect Matching