Jayaseree, R.; Kulandai Therese, A.; Mary, U. Eccentric connectivity index of thorny cycle graph and thorny star graph. (English) Zbl 1360.05039 J. Graph Label. 2, No. 2, 243-250 (2016). Summary: The graph invarient \(M_1\), known under the name first Zagreb index, equal to the sum of the squares of the degrees of the vertices of the respective graph. \(M_2\), the second Zagreb index is defined as the sum of the product of the end degrees of the edges of the respective graphs and \(M_3\), the third Zagreb index is the sum of the absolute value of the difference of the end degrees of the edges of the respecctive graphs. The eccentric connectivity index of a simple connected graph \(G\) is defined by the sum of the product of the degree and eccentricity of every vertex. The thorny graph of \(G\) is obtained by attaching a number of thorns to each vertex of \(G\). In this paper we derive the three Zagreb indices and explicit expression for the eccentric connectivity index of some thorny graphs such as thorny cycle graph and thorny star graph. MSC: 05C12 Distance in graphs 05C40 Connectivity Keywords:eccentric connectivity index; thorny graph PDFBibTeX XMLCite \textit{R. Jayaseree} et al., J. Graph Label. 2, No. 2, 243--250 (2016; Zbl 1360.05039)