Note: A simple criterion on degree sequences of graphs

Authors:
Amitabha Tripathi;Himanshu Tyagi
Affiliations:
Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India;Department of Electrical Engineering, Indian Institute of Technology, Hauz Khas, New Delhi-110016, India
Venue:
Discrete Applied Mathematics
Year:
2008

Citing 3
Cited 1

Seven criteria for integer sequences bring graphic

Journal of Graph Theory
A note on a theorem of Erdo's & Gallai

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Note: A short proof of a theorem on degree sets of graphs

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Note: A short constructive proof of A.R. Rao's characterization of potentially K r+1-graphic sequences

Discrete Applied Mathematics

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Abstract

A finite sequence of nonnegative integers is called graphic if the terms in the sequence can be realized as the degrees of vertices of a finite simple graph. We present two new characterizations of graphic sequences. The first of these is similar to a result of Havel-Hakimi, and the second equivalent to a result of Erdos & Gallai, thus providing a short proof of the latter result. We also show how some known results concerning degree sets and degree sequences follow from our results.