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Hamiltonian graphs with neighborhood intersections
Author(s) -
Chen G.,
Schelp R. H.
Publication year - 1994
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.3190180508
Subject(s) - combinatorics , mathematics , vertex (graph theory) , graph , hamiltonian (control theory) , discrete mathematics , mathematical optimization
In this paper, k + 1 real numbers c 1 , c 2 , ⃛, c k +1 are found such that the following condition is sufficient for a k ‐connected graph of order n to be hamiltonian: for each independent vertex set of k + 1 vertices in G .where S i = {v ≅ V:|N(v) ∩ S| = i} for 0 ≦ i ≦ k + 1. Such a set of k + 1 numbers is called an Hk ‐sequence. A sufficient condition for the existence of Hk ‐sequences is obtained that generalizes many known results involving sum of degrees, neighborhood unions, and/or neighborhood intersections.