Estimating the higher-order Randić index
نویسندگان
چکیده
Let G be a (molecular) graph with vertex set V 1⁄4 fv1;v2; . . . ;vng. Let dðv iÞ be the degree of the vertex v i 2 V . If the vertices v i1 ;v i2 ; . . . ;v ihþ1 form a path of length h;h P 1, in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1= ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi dðv i1 Þdðv i2 Þ; . . . ; dðv ihþ1 Þ q over all paths of length h contained (as subgraphs) in G. Lower and upper bounds for Rh are obtained, in terms of the vertex degree sequence of G. Closed formulas for Rh are obtained for the case when G is regular or semiregular bipartite. 2010 Elsevier B.V. All rights reserved.
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