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Non‐Cayley tetravalent metacirculant graphs and their Hamiltonicity
Author(s) -
Dac Tan Ngo
Publication year - 1996
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/(sici)1097-0118(199611)23:3<273::aid-jgt7>3.0.co;2-p
Subject(s) - cayley graph , combinatorics , mathematics , vertex transitive graph , graph , pancyclic graph , disjoint sets , odd graph , discrete mathematics , cayley transform , voltage graph , line graph , 1 planar graph
We define three families Φ 1 , Φ 2 and Φ 3 of special tetravalent metacirculant graphs and show that any non‐Cayley tetravalent metacirculant graph is isomorphic to a union of disjoint copies of a graph in one of the families Φ 1 , Φ 2 or Φ 3 . Using this result we prove further that every connected non‐Cayley tetravalent metacirculant graph has a Hamilton cycle. © 1996 John Wiley & Sons, Inc.