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Transactions of the American Mathematical Society
Article . 1932 . Peer-reviewed
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Proceedings of the National Academy of Sciences
Article . 1931 . Peer-reviewed
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Part of book or chapter of book . 2009 . Peer-reviewed
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Article . 1932 . Peer-reviewed
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Non-Separable and Planar Graphs

Non-separable and planar graphs
descriptionPublicationkeyboard_double_arrow_right Article , Part of book or chapter of book 01 Feb 1931Publisher:JSTORJournal:Transactions of the American Mathematical Society, volume 34, page 339 (issn: 0002-9947, Copyright policy )
Authors: Whitney, Hassler;

doi: 10.2307/1989545 , 10.1073/pnas.17.2.125 , 10.1007/978-0-8176-4842-8_2 , 10.1090/s0002-9947-1932-1501641-2

pmid: 16587624

pmc: PMC1076008

Non-Separable and Planar Graphs

Abstract

Introduction. In this paper the structure of graphs is studied by purely combinatorial methods. The concepts of rank and nullity are fundamental. The first part is devoted to a general study of non-separable graphs. Conditions that a graph be non-separable are given; the decomposition of a separable graph into its non-separable parts is studied; by means of theorems on circuits of graphs, a method for the construction of non-separable graphs is found, which is useful in proving theorems on such graphs by mathematical induction.

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Graph theory

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    selected citations
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    This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
    		 85
    popularity
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    		 Top 10%
    influence
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    impulse
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
85
Top 10%
Top 1%
Average
bronze