The Maximal ABC Index of the Corona of Two Graphs

Haiqin Liu and Yanling Shao

Mathematical Problems in Engineering, 2021, vol. 2021, 1-9

Abstract:

Let be the corona of two graphs and which is the graph obtained by taking one copy of and copies of and then joining the th vertex of to every vertex in the copy of . The atom-bond connectivity index (ABC index) of a graph is defined as , where is the edge set of and and are degrees of vertices and , respectively. For the ABC indices of with and being connected graphs, we get the following results. (1) Let and be connected graphs. The ABC index of attains the maximum value if and only if both and are complete graphs. If the ABC index of attains the minimum value, then and must be trees. (2) Let and be trees. Then, the ABC index of attains the maximum value if and only if is a path and is a star.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6699529

DOI: 10.1155/2021/6699529

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