On Detour Index
نویسندگان
چکیده
The detour index of a connected graph is defined as the sum of the detour distances (lengths of longest paths) between unordered pairs of vertices of the graph. We give bounds for the detour index, determine the graphs with minimum and maximum detour indices respectively in the class of n-vertex unicyclic graphs with cycle length r, where 3 ≤ r ≤ n−2, and the graphs with the first, the second and the third smallest and largest detour indices respectively in the class of n-vertex unicyclic graphs for n ≥ 5.
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