The Degree Sequence of Connected Graphs and the Number of Lower Degree Vertices of Connected Plannar Graphs
Lianying Miao · College Mathematics · 2009
The necessary and sufficient condition on which a degree sequence is a graph sequences is given by American mathematician Bondy.In this paper,after proving a necessary and sufficient condition on which a degree sequence is a sequence of connected graph,we gave a conception φ(n,m) which denotes the number of lower degree vertices of connected planar graphs,and for some small values of n,we obtained the corresponding φ(n,m).At last, we gave an upper and lower bound of φ(n,m).