View More View Less
  • 1 Department of Mathematics and Statistics Western Michigan University 49008-5152 Kalamazo Michigan USA
  • 2 Louisville
Restricted access

A graphH divides a graphG, writtenH|G, ifG isH-decomposable. A graphG without isolated vertices is a greatest common divisor of two graphsG 1 andG 2 ifG is a graph of maximum size for whichG|G 1 andG|G 2, while a graphH without isolated vertices is a least common multiple ofG 1 andG 2 ifH is a graph of minimum size for whichG 1|H andG 2|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 ofG 1 andG 2 to the product of their sizes can be arbitrarily large or arbitrarily small. Sizes of least common multiples of various pairsG 1,G 2 of graphs are determined, including when one ofG 1 andG 2 is a cycle of even length and the other is a star.

Monthly Content Usage

Abstract Views Full Text Views PDF Downloads
Sep 2020 2 0 0
Oct 2020 1 0 0
Nov 2020 1 0 0
Dec 2020 0 0 0
Jan 2021 9 0 0
Feb 2021 1 0 0
Mar 2021 2 0 0