Which numbers are status differences?

Hongying Lin and Bo Zhou

Applied Mathematics and Computation, 2021, vol. 399, issue C

Abstract: Given a connected graph G, the status sG(x) of a vertex x of G is the sum of the distances from x to all other vertices in G, and the status difference of G is sd(G)=maxx,y∈V(G)(sG(x)−sG(y)). The status difference is a useful descriptor in communication networks. We determine the numbers that can be the status differences of trees and connected graphs, respectively, with fixed order, and characterize the trees with the first a few smallest status differences when the order is fixed. Also, we identify the trees with maximum status difference over all trees with fixed maximum degree, number of leaves, and diameter, respectively, as well as the series-reduced trees with maximum status difference.

Keywords: Status difference; Minimum status; Maximum status; Number of leaves; Diameter; Series-reduced tree (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000527

DOI: 10.1016/j.amc.2021.126004

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