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On the number of cycles of length 4 in a maximal planar graph

✍ Scribed by Ahmad Fawzi Alameddine

Publisher: John Wiley and Sons
Year: 1980
Tongue: English
Weight: 148 KB
Volume: 4
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.3190040411

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✦ Synopsis

Abstract

Let p and C~4~ (G) be the number of vertices and the number of 4‐cycles of a maximal planar graph G, respectively. Hakimi and Schmeichel characterized those graphs G for which C~4~ (G) = 1/2(p^2^ + 3__p__ ‐ 22). This characterization is correct if p ≥ 9. However, for p = 7 or 8, there is exactly one other graph which violates the theorem in the sense that the upper bound of C~4~ (G) is also attained.

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