EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.)
Vol. 34(48), pp. 3--5 (1983)

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THE REGULATION NUMBER OF A GRAPH

Jin Akiyama, Frank Harary

Nippon Ika University Kawasaki, Japan and University of Michigen Ann Arbor, USA

Abstract: The regulation number $r(G)$ of a graph $G$ with maximum degree $d$ is defined as the smallest number of new points in a $d$-regular supergraph. It is shown that for $d\geq3$, every possible value of $r(G)$ between zero and the maximum established by Akiyama, Era and Harary, namely, $d$(mod 2)$+1+d$, is realized by some graph. Also, a characterization is given for $G$ to have $r(G)=n$.

Classification (MSC2000): 03B50

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Electronic fulltext finalized on: 3 Nov 2001. This page was last modified: 16 Nov 2001.

© 2001 Mathematical Institute of the Serbian Academy of Science and Arts
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