Group connectivity of graphs-A nonhomogeneous analogue of nowhere-zero flow properties

François Jaeger; Nathan Linial; Charles Payan; Michael Tarsi

doi:10.1016/0095-8956(92)90016-Q

Group connectivity of graphs-A nonhomogeneous analogue of nowhere-zero flow properties

François Jaeger^*
, Nathan Linial
, Charles Payan
, Michael Tarsi

^*Corresponding author for this work

The Rachel and Selim Benin School of Engineering and Computer Science

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

170 Scopus citations

Abstract

Let G = (V, E) be a digraph and f a mapping from E into an Abelian group A. Associated with f is its boundary ∂f, a mapping from V to A, defined by ∂f(x) = Σ_{e leaving x}f(e)-Σ_{e entering x}f(e). We say that G is A-connected if for every b: V → A with Σ_{x ∈ V}b(x)=0 there is an f: E → A - {0} with b = ∂f. This concept is closely related to the theory of nowhere-zero flows and is being studied here in light of that theory.

Original language	English
Pages (from-to)	165-182
Number of pages	18
Journal	Journal of Combinatorial Theory. Series B
Volume	56
Issue number	2
DOIs	https://doi.org/10.1016/0095-8956(92)90016-Q
State	Published - Nov 1992

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abstract = "Let G = (V, E) be a digraph and f a mapping from E into an Abelian group A. Associated with f is its boundary ∂f, a mapping from V to A, defined by ∂f(x) = Σe leaving xf(e)-Σe entering xf(e). We say that G is A-connected if for every b: V → A with Σx ∈ Vb(x)=0 there is an f: E → A - \{0\} with b = ∂f. This concept is closely related to the theory of nowhere-zero flows and is being studied here in light of that theory.",

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AU - Tarsi, Michael

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N2 - Let G = (V, E) be a digraph and f a mapping from E into an Abelian group A. Associated with f is its boundary ∂f, a mapping from V to A, defined by ∂f(x) = Σe leaving xf(e)-Σe entering xf(e). We say that G is A-connected if for every b: V → A with Σx ∈ Vb(x)=0 there is an f: E → A - {0} with b = ∂f. This concept is closely related to the theory of nowhere-zero flows and is being studied here in light of that theory.

AB - Let G = (V, E) be a digraph and f a mapping from E into an Abelian group A. Associated with f is its boundary ∂f, a mapping from V to A, defined by ∂f(x) = Σe leaving xf(e)-Σe entering xf(e). We say that G is A-connected if for every b: V → A with Σx ∈ Vb(x)=0 there is an f: E → A - {0} with b = ∂f. This concept is closely related to the theory of nowhere-zero flows and is being studied here in light of that theory.

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Group connectivity of graphs-A nonhomogeneous analogue of nowhere-zero flow properties

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