[PDF][PDF] Neighborhood complexes of some exponential graphs
N Nilakantan, S Shukla - arXiv preprint arXiv:1709.05263, 2017 - arxiv.org
N Nilakantan, S Shukla
arXiv preprint arXiv:1709.05263, 2017•arxiv.org… • If G and H are two graphs, then the exponential graph HG is defined to be the graph
where V (HG) contains all the set maps from V (G) to V (H). Any two vertices f and f/ in V (HG)
are said to be adjacent, if v ∼ v/ in G implies that f(v) ∼ f/(v/) in H. … From [5, Proposition 3.5]
we have a relationship between the exponential graph and the categorical product in the
Hom-complex. …
where V (HG) contains all the set maps from V (G) to V (H). Any two vertices f and f/ in V (HG)
are said to be adjacent, if v ∼ v/ in G implies that f(v) ∼ f/(v/) in H. … From [5, Proposition 3.5]
we have a relationship between the exponential graph and the categorical product in the
Hom-complex. …
In this article, we consider the bipartite graphs . We first show that the connectedness of . Further, we show that is homotopic to , if .
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