The Existence of Diameter-Edge-Critical Graphs
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This thesis investigates diameter-edge-critical graphs. Graphs are considered an excellent modelling tool for complex physical systems and many real world problems can be represented by graphs. An important problem that arises is that of characterizing graphs that satisfy certain properties representing the requirements of the system. The diameter of a graph is an important parameter in network design and analysis, as it provides information on the efficiency and the reliability of the network. This thesis establishes classes of diameter-edge-critical graphs that have applications in networks that arise in our high technology world.
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