Results 11 to 20 of about 4,754,290 (301)

Estimating the Vertex PI Index [PDF]

Zeitschrift für Naturforschung A, 2010
The vertex PI index is a distance-based molecular structure descriptor, that recently found numerous chemical applications. Lower and upper bounds for PI are obtained, as well as results of Nordhaus-Gaddum type.
Das, Ivan Gutman, Kinkar Ch
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The PI index of product graphs

Applied Mathematics Letters, 2008
The Padmakar–Ivan index of a graph G is the sum over all edges uv of G of number of edges which are not equidistant from u and v. In this work, an exact expression for the PI index of the Cartesian product of bipartite graphs is computed.
Yousefi-Azari, H., Manoochehrian, B., Ashrafi, A.R.   +2 more
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The PI index of phenylenes

Journal of Mathematical Chemistry, 2016
The Padmakar–Ivan (PI) index is a graph invariant defined as the summation of the sums of n eu (e|G) and n ev (e|G) over all the edges e = uv of a connected graph G, i.e., PI(G) = ∑ e∈E(G)[n eu (e|G) + n ev (e|G)], where n eu (e|G) is the number of edges
Deng, H, Chen, S, Zhang, J
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Bounds on Szeged and PI Indexes in terms of Second Zagreb Index [PDF]

, 2012
In this short note, we studied the vertex version and the edge version of the Szeged index and the PI index and obtained bounds for these indices in terms of the Second Zagreb index.
Ranjini P.S., Phani Raju, M., Lokesha, V.   +2 more
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Estimating the PI-Estrada index of graphs [PDF]

Discrete Mathematics Letters, 2021
Summary: Let \(G\) be a graph with \(n\) vertices. The PI-Estrada index of \(G\) is an invariant that is calculated from the eigenvalues of the vertex-PI matrix of \(G\). The main purpose of this paper is to establish upper and lower bounds for the PI-Estrada index of a graph in terms of the number of vertices, edges, triangles and pendant vertices.
Akbar Jahanbani, Hajar Shooshtari, Jonnathan Rodriguez   +2 more
doaj   +2 more sources

Bounds for the Co-PI Index of a Graph

, 2015
WOS: 000371149500001In this paper, we present some inequalities for the Co-PI index involving the some topological indices, the number of vertices and edges, and the maximum degree. After that, we give a result for trees.
Kaya, E., Maden, A. D.
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On the square PI index of graphs [PDF]

Discrete Mathematics Letters
Liju Alex, Ivan Gutman, Dariush Heidari, Mohammadreza Rostami   +3 more
doaj   +2 more sources

The vertex PI index and Szeged index of bridge graphs [PDF]

Discrete Applied Mathematics, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Toufik Mansour, Matthias Schork
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The PI Index of polyomino chains

Applied Mathematics Letters, 2008
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lixing Xu, Shubo Chen
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On Weighted PI Index of Graphs

Electronic Notes in Discrete Mathematics, 2016
Abstract The vertex PI index of a graph G, denoted by P I v ( G ) , is the sum over all edges uv of G of the number of vertices which are not equidistant from u and v. Similarly, the Weighted PI index of a graph G, denoted by P I w ( G ) = ∑ u v = e ∈ E ( G ) ( d G ( u ) + d G ( v
Kannan Pattabiraman, P. Kandan
openaire   +2 more sources