Maximum number of edges joining vertices on a cube

Authors:
Khaled A. S. Abdel-Ghaffar
Affiliations:
Department of Electrical and Computer Engineering, University of California, One Shields Ave., Davis, CA
Venue:
Information Processing Letters
Year:
2003

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Abstract

Let Ed(n) be the number of edges joining vertices from a set of n vertices on a d-dimensional cube, maximized over all such sets. We show that Ed(n) = Σi=0r-1 (li/2+i)2li, where r and l0 l1 ... lr-1 are nonnegative integers defined by n= Σi=0r-12li.