| Popis: |
For a real number α\alpha , the general Randić index of a graph GG, denoted by Rα(G){R}_{\alpha }\left(G), is defined as the sum of (d(u)d(v))α{\left(d\left(u)d\left(v))}^{\alpha } for all edges uvuv of GG, where d(u)d\left(u) denotes the degree of a vertex uu in GG. In particular, R−12(G){R}_{-\tfrac{1}{2}}\left(G) is the ordinary Randić index, and is simply denoted by R(G)R\left(G). Let α\alpha be a real number. In this article, we show that (1)if α≥0\alpha \ge 0, Rα(L(G))≥2Rα(G){R}_{\alpha }\left(L\left(G))\ge 2{R}_{\alpha }\left(G) for any graph GG with δ(G)≥3\delta \left(G)\ge 3;(2)if α≥0\alpha \ge 0, Rα(L(G))≥Rα(G){R}_{\alpha }\left(L\left(G))\ge {R}_{\alpha }\left(G) for any connected graph GG which is not isomorphic to Pn{P}_{n};(3)if α |
