Abstract
The 2-degree of a vertex v in a (molecular) graph G is the number of vertices which are at distance two from v in G. The first leap Zagreb index of a graph G is the sum of squares of the 2-degree of all vertices in G and the third leap Zagreb index of G is the sum of product of the degree and 2-degree of every vertex v in G. In this paper, we compute the first and third leap Zagreb indices of bridge and chain graphs. Also we apply these results to determine the first and third leap Zagreb indices of some chemical structures such as polyphenyl chains and spiro chains.
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