11 research outputs found
Network bipartivity and the transportation efficiency of European passenger airlines
The analysis of the structural organization of the interaction network of a complex system is central to understand its functioning. Here, we focus on the analysis of the bipartivity of graphs. We first introduce a mathematical approach to quantify bipartivity and show its implementation in general and random graphs. Then, we tackle the analysis of the transportation networks of European airlines from the point of view of their bipartivity and observe significant differences between traditional and low cost carriers. Bipartivity shows also that alliances and major mergers of traditional airlines provide a way to reduce bipartivity which, in its turn, is closely related to an increase of the transportation efficiency
The quotients between the (revised) Szeged index and Wiener index of graphs
Let and be the Szeged index, revised Szeged index and
Wiener index of a graph In this paper, the graphs with the fourth, fifth,
sixth and seventh largest Wiener indices among all unicyclic graphs of order
are characterized; as well the graphs with the first, second,
third, and fourth largest Wiener indices among all bicyclic graphs are
identified. Based on these results, further relation on the quotients between
the (revised) Szeged index and the Wiener index are studied. Sharp lower bound
on is determined for all connected graphs each of which contains
at least one non-complete block. As well the connected graph with the second
smallest value on is identified for containing at least one
cycle.Comment: 25 pages, 5 figure