The Bounds of Vertex Padmakar–Ivan Index on k-Trees
Department of Mathematics and Physics, Texas A&M International University, Laredo, TX 78041, USA
Institute of Computing Science and Technology, Guangzhou University, Guangzhou 510006, China
School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
Department of Mathematics, The University of Mississippi, University, MS 38677, USA
Author to whom correspondence should be addressed.
Received: 26 January 2019 / Revised: 11 March 2019 / Accepted: 11 March 2019 / Published: 1 April 2019
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The Padmakar–Ivan (
) index is a distance-based topological index and a molecular structure descriptor, which is the sum of the number of vertices over all edges
of a graph such that these vertices are not equidistant from u
. In this paper, we explore the results of
-indices from trees to recursively clustered trees, the k
-trees. Exact sharp upper bounds of PI indices on k
-trees are obtained by the recursive relationships, and the corresponding extremal graphs are given. In addition, we determine the
-values on some classes of k
-trees and compare them, and our results extend and enrich some known conclusions.
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MDPI and ACS Style
Wang, S.; Shao, Z.; Liu, J.-B.; Wei, B. The Bounds of Vertex Padmakar–Ivan Index on k-Trees. Mathematics 2019, 7, 324.
Wang S, Shao Z, Liu J-B, Wei B. The Bounds of Vertex Padmakar–Ivan Index on k-Trees. Mathematics. 2019; 7(4):324.
Wang, Shaohui; Shao, Zehui; Liu, Jia-Bao; Wei, Bing. 2019. "The Bounds of Vertex Padmakar–Ivan Index on k-Trees." Mathematics 7, no. 4: 324.
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