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Minimum detour index of cactus graphs. (English) Zbl 1449.05152

Summary: 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. A cactus is a connected graph in which no edge lies in more than one cycle. In this paper, we characterize the first two smallest detour indices among all cactus graphs and which attain the bounds.

MSC:

05C38 Paths and cycles
05C12 Distance in graphs
05C09 Graphical indices (Wiener index, Zagreb index, Randić index, etc.)