On leap eccentric connectivity index of thorny graphs

The 2-degree of a vertex v of a simple graph G is the number of vertices which are at distance two from v in G and is denoted by d2(v). In this article, we compute exact values of a recent eccentricity-based topological index called Leap eccentric connectivity index (LECI), which is defined as the sum of product of 2-degree and eccentricity of every vertex in G, for some special classes of thorny graphs namely, thorny complete graph, thorny complete bipartite graph, thorny cycles and thorny paths. Also we discuss some of its applications in chemical structures such as cyclo-alkanes.