Abstract
Graph theory is the fundamental basis of the neural networks. This paper reports the investigation work of the relationships between artificial neural networks and graph theory, and presents the analysis of the specific issues relating to the change of the geodetic number due to operations on the graphs. Recent research work on the geodetic number of graphs has been found in the literature. Determining the geodetic number of arbitrary graph can be proved to be NP-hard. However, a fundamental issue in graph theory concerns how a parameter value is affected after small changes executed to the graph. This issue is analyzed in the authors' research by adding or contracting an edge to the graph.
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