Abstract
Let ℒ(G) and V(G) be, respectively, the closed-set lattice and the vertex set of a graph G. Any lattice isomorphism Φ: ℒV(G)≃ℒ(G′) induces a bijection ϕ: V(G)→V(G′) such that for each x in V(G), ϕ(x)=x' in V(G') iff Φ({x})={x'}. A graph G is strongly sensitive if for any graph G' and any lattice isomorphism Φ: ℒ(G)≃ℒ(G′), the bijection ϕ induced by Φ is a graph isomorphism of G onto G'. In this paper we present some sufficient conditions for graphs to be strongly sensitive and prove in particular that all C4-free graphs and all covering graphs of finite lattices are strongly sensitive.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
