Randić ordering of chemical trees

On the Extremal Zagreb Indices of Graphs with Cut Edges

“…The first paper in which the Randić connectivity index was used in QSAR appeared soon after the original publication, also in [29]. Mathematicians too exhibited considerable interest in the properties of the Randić connectivity index; see [5,6,17,18,31,32,42,44]. The Randić connectivity index has also evolved into several variants [16,37,38,43,[46][47][48][49].…”

“…In fact, an investigation of the above problems mainly deals with graphs whose cyclomatic number is at most 2 as the sole objects [12,15,25,30,35,44,50,54]; Mathematical and computational properties of Zagreb indices have also been considered [8,14,21,23,39,40,55,56]. Other directions of investigation include studies of the relation between M 1 (G) (respectively, M 2 (G)) and the corresponding invariant of elements of the graph G (vertices, pendent vertices, diameter, maximum degree, girth, perfect matching); see [9,12,13,25,30,33,34,50,55,56].…”

On the Maximum Zagreb Indices of Graphs with k Cut Vertices

“…The first paper in which the Randić connectivity index was used in QSAR appeared soon after the original publication, also in [34]. Mathematicians too exhibited considerable interest in the properties of the Randić connectivity index; see [8,9,21,22,36,37,44,45,47]. The Randić connectivity index has also evolved into several variants [20,46,49,50] The research is supported in part by National Science The Randić connectivity index has been extended as the general Randić connectivity index and general zeroth-order Randić connectivity index, and then the Zagreb indices appear to be the special cases of them [11,13,14,19,25,29,37].…”

“…In fact, investigation of the above problems mainly deal with graphs whose cyclomatic number is at most 2 as the sole objects [15,18,30,35,40,47,51,55]; Mathematical and computational properties of Zagreb indices have also been considered [17,27,43,56,57]. Other direction of investigation include studies of relation between M 1 (G) (respectively, M 2 (G)) and the corresponding invariant of elements of the graph G (order, cut edges, pendent vertices, diameter, maximum degree, girth, perfect matching); see [12,15,16,30,35,38,39,51,56,57].…”

Variation of the Wiener index under tree transformations

“…Finally, following the main ideas of [14], another application of u ( ) and v ( ) is considered in Section 3. Based on the maximal subtree transformations, we show how to construct in T n , the class of trees with n vertices, a sequence of trees {T j } k j =0 such that T j +1 is obtained from T j by one of these transformations and W (T j ) < W (T j +1 ).…”