Diameter Bounds for Planar Graphs

The inverse degree of a graph is the sum of the reciprocals of the degrees of its vertices. We prove that in any connected planar graph, the diameter is at most 5/2 times the inverse degree, and that this ratio is tight. To develop a crucial surgery method, we begin by proving the simpler related upper bounds (4(vertical bar V vertical bar - 1) - vertical bar E vertical bar)/3 and 4 vertical bar V vertical bar(2)/3 vertical bar E vertical bar on the diameter (for connected planar graphs), which are also tight. (C) 2010 Elsevier B.V. All rights reserved.


Published in:
Discrete Mathematics, 311, 5, 327–335
Year:
2011
Publisher:
Elsevier
ISSN:
0012-365X
Keywords:
Laboratories:




 Record created 2010-12-30, last modified 2018-03-18

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