Abstract
Let G be a graph with vertex set V=(v1,v2,…,vn). Let δ(vi) be the degree of the vertex vi∈V. If the vertices vi1,vi2,…,vih+1 form a path of length h≥1 in the graph G, then the hth order Randić index Rh of G is defined as the sum of the terms 1/δ(vi1)δ(vi2)⋯δ(vih+1) over all paths of length h contained (as subgraphs) in G. Lower and upper bounds for Rh, in terms of the vertex degree sequence of its factors, are obtained for corona product graphs. Moreover, closed formulas are obtained when the factors are regular graphs.
Highlights
Research Article On the Randic Index of Corona Product GraphsDepartamento d’Enginyeria Informatica i Matematiques, Universitat Rovira i Virgili, Avinguda Paısos Catalans 26, 43007 Tarragona, Spain
In this work we consider simple graphs G V, E with n vertices and m edges
For every vertex vi ∈ V, δ vi represents the degree of the vertex vi in G
Summary
Departamento d’Enginyeria Informatica i Matematiques, Universitat Rovira i Virgili, Avinguda Paısos Catalans 26, 43007 Tarragona, Spain. Let G be a graph with vertex set V v1, v2, . Let δ vi be the degree of the vertex vi ∈ V. Vih 1 form a path of length h ≥ 1 in the graph G, the hth order Randicindex Rh of G is defined as the sum of the terms 1/ δ vi[1] δ vi2 · · · δ vih 1 over all paths of length h contained as subgraphs in G. Lower and upper bounds for Rh, in terms of the vertex degree sequence of its factors, are obtained for corona product graphs. Closed formulas are obtained when the factors are regular graphs
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