FINITE SIMPLE GRAPHS AND THEIR ASSOCIATED GRAPH LATTICES
Abstract
LetG=(V,E)be a graph with vertex set V and an edge set E; and let Ω(G) be the lattice of open set for classical topology partially ordered by subset inclusion. Ω(G) contains a wealth of information about the graph G, and there is a subposet of Ω(G) which can be used to reconstruct (a graph-isomorphic copy of) the graph complement of G. In this resesarch work,we go a step further and examine some aspect of the open set lattice induced by these topological spaces via exploration of their structure and most importantly show that; these lattices contain information necessary to reconstruct the graph and its complemenet in several ways.
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