Premium
Pancyclicity and extendability in strong products
Author(s) -
Ramachandran S.,
Parvathy R.
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(199605)22:1<75::aid-jgt10>3.0.co;2-n
Subject(s) - combinatorics , mathematics , graph , vertex (graph theory) , pancyclic graph , hamiltonian (control theory) , hamiltonian path , wheel graph , discrete mathematics , graph power , line graph , 1 planar graph , mathematical optimization
In this paper, we first prove that for any connected graph G with at least two vertices, there is an integer m for which the strong product X⌅ G m has pancyclic ordering from each vertex. After characterizing the graphs G for which G X⌅ K 2 is Hamiltonian, we determine a criterion for extendability of cycles. We also prove that if G is a connected, K 1.3 ‐free graph with δ ≥ 2, then GX ⌅X K 2 is fully cycle extendable as well as 1‐edge Hamiltonian. © 1996 John Wiley & Sons, Inc.