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Hamming distance of a two bit strings u and v of length n is defined to be the number of positions of u and v with different digit. If G is a simple graph on n vertices and m edges and B is an edge–vertex incidence matrix of G, then every edge e of G can be labeled using a binary digit string of length n from the row of B which corresponds to the edge e. We discuss Hamming distance of two different edges of the graph G. Then, we present formulae for the sum of all Hamming distances between two different edges of G, particularly when G is a path, a cycle, and a wheel, and some composite graphs.

This paper presents an alternative approach to evaluating the overall efficiency and performance of Taiwanese container ports. Specifically, a parallel activity with series structure concept in the form of data envelopment analysis (MNDEA) is used to construct a model that applies to three different activities: harbor management, stevedoring and warehousing operations. We will further divide each activity into two process types, production processes and services processes. We will also adopt a Delphi survey approach and use the Analytic Network Process (ANP) to identify these processes’influence dependence and their degree of importance for the MNDEA model setting. An empirical application demonstrates the performance of Taiwanese container ports by using MNDEA with window analysis techniques via the directional distance functionThe results demonstrate that the application is effective in indicating and/or suggesting resource-adjustments, while considering which undesirable output levels and shared inputs were involved. The results also present directions for possible improvements in workplace efficiency.