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An Euler-type formula for

✍ Scribed by Michael J. Dancs; Tian-Xiao He


Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
86 KB
Volume
118
Category
Article
ISSN
0022-314X

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✦ Synopsis


In this short paper, we give several new formulas for ΞΆ(n) when n is an odd positive integer. The method is based on a recent proof, due to H. Tsumura, of Euler's classical result for even n. Our results illuminate the similarities between the even and odd cases, and may give some insight into why the odd case is much more difficult.


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Let G be a median graph on n vertices and m edges and let k be the number of equivalence classes of the Djokovi6's relation ~9 defined on the edge-set of G. Then 2n-m-k ~< 2. Moreover, 2n-m-k = 2 if and only if G is cube-free. (~) 1998 Elsevier Science B.V. All rights reserved A median graph is a co