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  • 1 Department of Mathematics and Statistics Western Michigan University 49008-5152 Kalamazo Michigan USA
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A graphH divides a graphG, writtenH|G, ifG isH-decomposable. A graphG without isolated vertices is a greatest common divisor of two graphsG1 andG2 ifG is a graph of maximum size for whichG|G1 andG|G2, while a graphH without isolated vertices is a least common multiple ofG1 andG2 ifH is a graph of minimum size for whichG1|H andG2|H. It is shown that every two nonempty graphs have a greatest common divisor and least common multiple. It is also shown that the ratio of the product of the sizes of a greatest common divisor and least common multiple ofG1 andG2 to the product of their sizes can be arbitrarily large or arbitrarily small. Sizes of least common multiples of various pairsG1,G2 of graphs are determined, including when one ofG1 andG2 is a cycle of even length and the other is a star.

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Periodica Mathematica Hungarica
Language English
Size B5
Year of
Foundation
1971
Volumes
per Year
2
Issues
per Year
4
Founder Bolyai János Matematikai Társulat - János Bolyai Mathematical Society
Founder's
Address
H-1055 Budapest, Hungary Falk Miksa u. 12.I/4.
Publisher Akadémiai Kiadó
Springer Nature Switzerland AG
Publisher's
Address
H-1117 Budapest, Hungary 1516 Budapest, PO Box 245.
CH-6330 Cham, Switzerland Gewerbestrasse 11.
Responsible
Publisher
Chief Executive Officer, Akadémiai Kiadó
ISSN 0031-5303 (Print)
ISSN 1588-2829 (Online)

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