Minimum statuses of connected graphs with fixed maximum degree and order

Chiang Lin (), Wei-Han Tsai, Jen-Ling Shang () and Yuan-Jen Zhang
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Chiang Lin: National Central University
Wei-Han Tsai: National Central University
Jen-Ling Shang: Kainan University
Yuan-Jen Zhang: National Central University

Journal of Combinatorial Optimization, 2012, vol. 24, issue 3, No 1, 147-161

Abstract: Abstract The status of a vertex in a connected graph is the sum of distances between the vertex and all vertices. The minimum status of a connected graph is the minimum of statuses of all vertices of this graph. In this paper we obtain the sharp lower bound and the sharp upper bound on the minimum status of a connected graph with maximum degree k and order n. All the graphs attaining the lower bound are obtained, and a necessary condition is given for those graphs attaining the upper bound.

Keywords: Status; Minimum status; Tree; Median; Balanced k-tree; k-grass (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s10878-011-9412-4

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