| Summary: | Let G1∘G2 be the corona of two graphs G1 and G2 which is the graph obtained by taking one copy of G1 and VG1 copies of G2 and then joining the ith vertex of G1 to every vertex in the i th copy of G2. The atom-bond connectivity index (ABC index) of a graph G is defined as ABCG=∑uv∈EGdGu+dGv−2/dGudGv, where EG is the edge set of G and dGu and dGv are degrees of vertices u and v, respectively. For the ABC indices of G1∘G2 with G1 and G2 being connected graphs, we get the following results. (1) Let G1 and G2 be connected graphs. The ABC index of G1∘G2 attains the maximum value if and only if both G1 and G2 are complete graphs. If the ABC index of G1∘G2 attains the minimum value, then G1 and G2 must be trees. (2) Let T1 and T2 be trees. Then, the ABC index of T1∘T2 attains the maximum value if and only if T1 is a path and T2 is a star.
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