Principal common divisors of graphs

Gary Chartrand; Wayne Goddard; Michael A. Henning; Farrokh Saba; Henda C. Swart

doi:10.1006/eujc.1993.1012

Principal common divisors of graphs

Gary Chartrand, Wayne Goddard, Michael A. Henning, Farrokh Saba, Henda C. Swart

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

A graph H divides a graph G, written H | G, if G is H-decomposable. If H ≠ G, then H properly divides G. A graph G is a principal common divisor if there exist graphs G₁ and G₂ such that G properly divides G₁ and G₂, and if H is any graph such that H | G₁ and H | G₂, then H | G. Several graphs that are principal common divisors are described. It is shown that complete graphs are not principal common divisors.

Original language	English
Pages (from-to)	85-93
Number of pages	9
Journal	European Journal of Combinatorics
Volume	14
Issue number	2
DOIs	https://doi.org/10.1006/eujc.1993.1012
Publication status	Published - Mar 1993
Externally published	Yes

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics

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abstract = "A graph H divides a graph G, written H | G, if G is H-decomposable. If H ≠ G, then H properly divides G. A graph G is a principal common divisor if there exist graphs G1 and G2 such that G properly divides G1 and G2, and if H is any graph such that H | G1 and H | G2, then H | G. Several graphs that are principal common divisors are described. It is shown that complete graphs are not principal common divisors.",

author = "Gary Chartrand and Wayne Goddard and Henning, {Michael A.} and Farrokh Saba and Swart, {Henda C.}",

year = "1993",

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AU - Chartrand, Gary

AU - Goddard, Wayne

AU - Henning, Michael A.

AU - Saba, Farrokh

AU - Swart, Henda C.

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N2 - A graph H divides a graph G, written H | G, if G is H-decomposable. If H ≠ G, then H properly divides G. A graph G is a principal common divisor if there exist graphs G1 and G2 such that G properly divides G1 and G2, and if H is any graph such that H | G1 and H | G2, then H | G. Several graphs that are principal common divisors are described. It is shown that complete graphs are not principal common divisors.

AB - A graph H divides a graph G, written H | G, if G is H-decomposable. If H ≠ G, then H properly divides G. A graph G is a principal common divisor if there exist graphs G1 and G2 such that G properly divides G1 and G2, and if H is any graph such that H | G1 and H | G2, then H | G. Several graphs that are principal common divisors are described. It is shown that complete graphs are not principal common divisors.

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Principal common divisors of graphs

Abstract

ASJC Scopus subject areas

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