CAYLEY GRAPHS OF PARTIALLY ORDERED SETS
2013 ◽
Vol 12
(04)
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pp. 1250184
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In this paper, we introduce the Cayley graph of a partially ordered set (poset). Let (P, ≤) be a poset, and let S be a subset of P. We define the undirected Cayley graph of P, denoted by Cay (P, S), as a graph with vertex-set P and edge-set E consisting of those sets {x, y} such that y ∈ {x, s}ℓ or x ∈ {y, s}ℓ for some s ∈ S, where for a subset T of P, Tℓ is the set of all x ∈ P such that x ≤ t, for all t ∈ T. We study some basic properties of Cay (P, S) such as connectivity, diameter and girth.
1979 ◽
Vol 27
(4)
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pp. 495-506
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1976 ◽
Vol 28
(4)
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pp. 820-835
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Keyword(s):
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2004 ◽
Vol 2004
(40)
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pp. 2145-2147
1964 ◽
Vol 16
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pp. 136-148
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1980 ◽
Vol 23
(2)
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pp. 231-236
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