On the number of cycles of length 4 in a maximal planar graph
Ahmad Fawzi Alameddine · Journal of Graph Theory · 1980
Abstract Let p and C4 (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 C4 (G) = 1/2(p2 + 3p ‐ 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 C4 (G) is also attained.