ON THE VARIATION OF THE RANDIC INDEX OF TRIANGLE-FREE GRAPHS

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Liu, J. (2013). ON THE VARIATION OF THE RANDIC INDEX OF TRIANGLE-FREE GRAPHS. Asian Journal of Current Engineering and Maths, 2(4). Retrieved from http://innovativejournal.in/index.php/ajcem/article/view/188
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Abstract

The variation of the Randic index of a graph G is defined as R , where d(u) denotes the degree of a vertex u in G. This index was first introduced in the paper [Dvorak Z., Lidick\'y B., Skrekovski R. (2011) Randic index and the diameter of a graph, European J. Combin. 32, 434-442.] as a mean to solve a conjecture of the Randic index. In this work, we give an equivalent expression for this index. Using this expression, we give the minimum value of the variation of the Randic index for any triangle-free graphs with order n and minimum degree for and show the corresponding extremal graph is the complete bipartite graph Kk,n-k.

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