Some extremal graphs with respect to the zeroth-order general Randić index. (English) Zbl 1452.05092
Summary: For a given graph set \(\mathcal{G}_n\), it is important to find the upper and lower bounds for some graph invariant in \(\mathcal{G}_n\) and characterize the graphs in which the maximal and minimal values are attained, respectively. In this paper, we investigated several upper and lower bounds on the general zeroth-order Randić index of graphs in terms of number of cut edges, independence number and matching number, respectively. The extremal graphs are also completely characterized.
MSC:
| 05C35 | Extremal problems in graph theory |
| 05C09 | Graphical indices (Wiener index, Zagreb index, Randić index, etc.) |
| 05C69 | Vertex subsets with special properties (dominating sets, independent sets, cliques, etc.) |
| 05C70 | Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) |
