Abstract
Let G be a connected bipartite graph with a perfect matching and the minimum degree at least two. The concept of an anti-forcing edge in G was introduced by Li in Li (1997). One known generalized version for an anti-forcing edge is an anti-forcing set S, which is a set of edges of G such that the spanning subgraph G−S has a unique perfect matching. In this paper, we introduce a new generalization of an anti-forcing edge: an anti-forcing path and an anti-forcing cycle. We show that the existence of an anti-forcing edge in G is equivalent to the existence of an anti-forcing path or an anti-forcing cycle in G. Then we show that G has an edge that is both forcing and anti-forcing if and only if G is an even cycle. In addition, e-anti-forcing paths and e-anti-forcing cycles in hexagonal systems are identified. The parallel concepts of forcing-paths and forcing-cycles of G are also presented.
Original language | English (US) |
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Pages (from-to) | 70-77 |
Number of pages | 8 |
Journal | Discrete Applied Mathematics |
Volume | 244 |
DOIs | |
State | Published - Jul 31 2018 |
All Science Journal Classification (ASJC) codes
- Discrete Mathematics and Combinatorics
- Applied Mathematics