Note on vertex degrees of planar graphs
Miroslaw Truszczyáski · Journal of Graph Theory · 1984
In this note the second moment of the vertex degree sequence of planar graphs is considered. We prove that 1 If G is an outerplanar graph of order n ⩾ 3 then 2 If G is a planar graph of order n ⩾ 4 then where d1,…,dn is the vertex degree sequence of G. We exhibit all graphs for which these upper bounds are attained.