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Note on PI and Szeged indices
In theoretical chemistry molecular structure descriptors are used for
modeling physico-chemical, pharmacological, toxicologic, biological and other
properties of chemical compounds. In this paper we study distance-based graph
invariants and present some improved and corrected sharp inequalities for PI,
vertex PI, Szeged and edge Szeged topological indices, involving the number of
vertices and edges, the diameter, the number of triangles and the Zagreb
indices. In addition, we give a complete characterization of the extremal
graphs.Comment: 10 pages, 3 figure
Cacti with Extremal PI Index
The vertex PI index is a
distance-based molecular structure descriptor, where denotes the
number of vertices which are closer to the vertex than to the vertex
and which has been the considerable research in computational chemistry dating
back to Harold Wiener in 1947. A connected graph is a cactus if any two of its
cycles have at most one common vertex. In this paper, we completely determine
the extremal graphs with the largest and smallest vertex PI indices among all
the cacti. As a consequence, we obtain the sharp bounds with corresponding
extremal cacti and extend a known result.Comment: Accepted by Transactions on Combinatorics, 201
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