Vertices of localized imbalance in a biased graph
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- by Thomas Zaslavsky PDF
- Proc. Amer. Math. Soc. 101 (1987), 199-204 Request permission
Abstract:
A biased graph consists of a graph $\Gamma$ and a subclass $\mathcal {B}$ of the polygons of $\Gamma$, such that no theta subgraph of $\Gamma$ contains exactly two members of $\mathcal {B}$. A subgraph is balanced when all its polygons belong to $\mathcal {B}$. A vertex is a balancing vertex if deleting it leaves a balanced graph. We give a construction for unbalanced biased graphs having a balancing vertex and we show that an unbalanced biased graph having more than one balancing vertex is an unbalanced series or parallel connection of balanced graphs.References
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Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 199-204
- MSC: Primary 05C75
- DOI: https://doi.org/10.1090/S0002-9939-1987-0897095-1
- MathSciNet review: 897095