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.) |