IJPAM: Volume 103, No. 1 (2015)


Aysun Aytac$^1$, Betul Atay$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Ege University
35100, Bornova, Izmir, TURKEY

Abstract. Networks are known to be prone to node or link failures. A central issue in the analysis of complex networks is the assessment of their robustness and vulnerability. A network is usually represented by an undirected simple graph where vertices represent processors and edges represent links between processors. Different approaches to properly define a measure for graph vulnerability has been proposed so far.

The distance d(i,j) between any two vertices i and j in a graph is the number of edges in a shortest path between i and j. If there is no path connecting i and j, then $d(i, j) =\infty$ . Latora and Marchiori introduced the measure of efficiency between vertices in a graph in 2001. The unweighted efficiency between two vertices i and j is defined to be $\varepsilon_{ij=1/d_{ij}}$ for all $i \neq j $. The global efficiency of a graph $E_{glob}=\frac{2}{n(n-1)}\sum\limits_{i \neq j}\varepsilon(v_i, v_j)$ which is simply the average of the efficiencies over all pairs of distinct $n$ vertices. In this paper, we study the global efficiency of special graphs. The behavior of this distance-related parameter on special graphs is taken into account by graphical analysis.

Received: March 13, 2015

AMS Subject Classification: 05C40, 68M10, 68R10

Key Words and Phrases: graph vulnerability, network design and communication, efficiency, global efficiency

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DOI: 10.12732/ijpam.v103i1.5 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 1
Pages: 61 - 70

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CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).