Diametral Paths in Total Graphs of Paths, Cycles and Stars
Keywords:Diametral path, Path, Cycle, Star, Diameter, Total graph
The diametral path of a graph is the shortest path between two vertices which has length equal to diameter of that graph. Total graph of a graph is a graph that has vertices representing all vertices and edges of the original graph and edges representing every vertex-vertex adjacency, edge-edge adjacency and edge-vertex incidence. In this paper, the number of diametral paths is determined for the paths, cycles and stars and their total graphs.
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