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Note on vertex degrees of planar graphs
Author(s) -
Truszczyáski Miroslaw
Publication year - 1984
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190080120
Subject(s) - combinatorics , mathematics , outerplanar graph , planar graph , vertex (graph theory) , 1 planar graph , discrete mathematics , graph , pathwidth , chordal graph , line graph
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 then2 If G is a planar graph of order n ⩾ 4 then where d 1 ,…, d n is the vertex degree sequence of G . We exhibit all graphs for which these upper bounds are attained.