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The effects of distance and neighborhood union conditions on hamiltonian properties in graphs
Author(s) -
Lindquester Terri England
Publication year - 1989
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190130309
Subject(s) - mathematics , combinatorics , hamiltonian (control theory) , graph , hamiltonian path , discrete mathematics , mathematical optimization
We prove that a 2‐connected graph G of order p is hamiltonian if for all distinct vertices u and v , dist( u,v ) = 2 implies that |N( u ) U N( v )| ⩾ (2 p ‐ 1)/3. We also demonstrate hamiltonian‐connected and traceability properties in graphs under similar conditions.
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