Counting the number of dissociation sets in cubic graphs - Jianhua Tu; Junyi Xiao; Rongling Lang (AIMS Mathematics, 2023)
Let $ G $ be a graph. A dissociation set of $ G $ is a subset of vertices that induces a subgraph with vertex degree at most 1. The dissociation polynomial of $ G $ is $ D_{G}(λ) = \sum_{D \in \mathcal{D}(G)} λ^{|D|} $, where $ \mathcal{D}(G) $ is the set of all dissociation sets of $ G $. In this paper, we prove that for any cubic graph $ G $ and any $ λ \in(0, 1] $,