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The Maximal ABC Index of the Corona of Two Graphs

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  • Haiqin Liu
  • Yanling Shao

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.

Suggested Citation

  • Haiqin Liu & Yanling Shao, 2021. "The Maximal ABC Index of the Corona of Two Graphs," Mathematical Problems in Engineering, Hindawi, vol. 2021, pages 1-9, April.
    • Handle: RePEc:hin:jnlmpe:6699529
    DOI: 10.1155/2021/6699529
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