116 research outputs found

    Cacti with Extremal PI Index

    Full text link
    The vertex PI index PI(G)=βˆ‘xy∈E(G)[nxy(x)+nxy(y)]PI(G) = \sum_{xy \in E(G)} [n_{xy}(x) + n_{xy}(y)] is a distance-based molecular structure descriptor, where nxy(x)n_{xy}(x) denotes the number of vertices which are closer to the vertex xx than to the vertex yy 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
    • …
    corecore