Geodesic
On Sums of Valencies in Planar Graphs
Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 111-114

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Planarity in graphs implies relatively small valencies and numbers of edges. In this note we find the maximum sum of valencies and the maximum number of incident edges for a set of n vertices in a planar graph with v vertices. Graphs considered are without multiple edges or loops. 
Bowen, Robert. On Sums of Valencies in Planar Graphs. Canadian mathematical bulletin, Tome 9 (1966) no. 1, pp. 111-114. doi: 10.4153/CMB-1966-016-x
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     author = {Bowen, Robert},
     title = {On {Sums} of {Valencies} in {Planar} {Graphs}},
     journal = {Canadian mathematical bulletin},
     pages = {111--114},
     year = {1966},
     volume = {9},
     number = {1},
     doi = {10.4153/CMB-1966-016-x},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1966-016-x/}
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