Please use this identifier to cite or link to this item: https://ir.swu.ac.th/jspui/handle/123456789/14888
ชื่อเรื่อง: The hamiltonian number of cubic graphs
ผู้แต่ง: Thaithae S.
Punnim N.
Keywords: Computation theory
Computational geometry
Differential equations
Hamiltonians
Connected graph
Cubic graph
Hamiltonian numbers
Integer-N
Line segment
Positive integers
Graph theory
วันที่เผยแพร่: 2008
บทคัดย่อ: A Hamiltonian walk in a connected graph G of order n is a closed spanning walk of minimum length in G. The Hamiltonian number h(G) of a connected graph G is the length of a Hamiltonian walk in G. Thus h may be considered as a measure of how far a given graph is from being Hamiltonian. We prove that if G runs over the set of connected cubic graphs of order n and n ≠ 14then the values h(G) completely cover a line segment [a,b] of positive integers. For an even integer n ≥ 4, let C(3n) be the set of all connected cubic graphs of order n. We define min(h,3n = min{h(G): G ∈ C(3n)} and max(h, 3n = max{h(G):G ∈ C(3n)}. Thus for an even integer n ≥ 4, the two invariants min (h, 3n ) and max (h,3 n ) naturally arise. Evidently, min (h, 3n ) = n. The exact values of max (h, 3n ) are obtained in all situations. © 2008 Springer Berlin Heidelberg.
URI: https://ir.swu.ac.th/jspui/handle/123456789/14888
https://www.scopus.com/inward/record.uri?eid=2-s2.0-70349929486&doi=10.1007%2f978-3-540-89550-3_23&partnerID=40&md5=1a057405b6f6e578cca0cf70e9d00812
ISSN: 3029743
Appears in Collections:Scopus 1983-2021

Files in This Item:
There are no files associated with this item.


Items in SWU repository are protected by copyright, with all rights reserved, unless otherwise indicated.