Particularly, the first and second Zagreb indices of a graph were introduced by chemists Gutman, Trinajstić and Ruscić . Subsequently, indicating their significance, numerous researchers have further explored the concepts initially presented in these seminal papers. For instance, in a recent publication , the authors introduced graph invariants known as the first and second leap Zagreb indices, also referred to as Zagreb connection indices. These indices are derived from the concept of the second degree of a vertex v, defined as follows: here, τ v denotes the count of a vertex's second neighbors, encompassing all vertices in G situated at a distance of two from v. Additionally, the authors investigated several general mathematical properties associated with these indices and their connection with other pertinent quantities within chemical graph theory was elucidated in .