Fundamental group and cycle space of dual graphs and applications. (English) Zbl 1197.05034
Summary: In this work, we study the fundamental group of the dual graph of a planar graph. Moreover, we show that a planar graph \(G\) has no cut vertex if and only if \(N(\Pi (D(G))) = N(\Pi (D(G - v))) - 1\) for any \(v \in V(G)\). Some applications relevant to quantum space time are indicated. Our results generalize and extend results in [S.I. Nada and E.H. Hamouda, “Fundamental group of dual graphs and applications to quantum space time”, Chaos Soliton Fractals 42, 500–503 (2009)].
MSC:
| 05C10 | Planar graphs; geometric and topological aspects of graph theory |
| 81R40 | Symmetry breaking in quantum theory |
References:
| [1] | Nada, S. I.; Hamouda, E. H., Fundamental group of dual graphs and applications to quantum space time, Chaos Soliton Fractals, 42, 500-503 (2009) · Zbl 1198.05132 |
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