scholarly journals ORDERING CATACONDENSED HEXAGONAL SYSTEMS WITH RESPECT TO VDB TOPOLOGICAL INDICES

2017 ◽  
Vol 23 (1) ◽  
pp. 277-289
Author(s):  
Juan Rada
Keyword(s):  
Topological Index ◽  
Topological Indices ◽  
Vertex Degree ◽  
Extremal Values ◽  
Hexagonal Systems

In this paper we give a complete description of the ordering relations in the set of catacondensed hexagonal systems, with respect to a vertex-degree-based topological index. As a consequence, extremal values of vertex-degree-based topological indices in special subsets of the set of catacondensed hexagonal systems are computed.

scholarly journals Sharp Upper and Lower Bounds of VDB Topological Indices of Digraphs

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1903
Author(s):  
Juan Monsalve ◽  
Juan Rada
Keyword(s):  
Lower Bounds ◽  
Topological Index ◽  
General Setting ◽  
Upper Bounds ◽  
Topological Indices ◽  
Vertex Degree ◽  
Upper And Lower Bounds ◽  
Lower And Upper Bounds ◽  
Extremal Values

A vertex-degree-based (VDB, for short) topological index φ induced by the numbers φij was recently defined for a digraph D, as φD=12∑uvφdu+dv−, where du+ denotes the out-degree of the vertex u,dv− denotes the in-degree of the vertex v, and the sum runs over the set of arcs uv of D. This definition generalizes the concept of a VDB topological index of a graph. In a general setting, we find sharp lower and upper bounds of a symmetric VDB topological index over Dn, the set of all digraphs with n non-isolated vertices. Applications to well-known topological indices are deduced. We also determine extremal values of symmetric VDB topological indices over OTn and OG, the set of oriented trees with n vertices, and the set of all orientations of a fixed graph G, respectively.

scholarly journals On extremal bipartite graphs with a given connectivity

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1531-1540
Author(s):  
Hanlin Chen ◽  
Hanyuan Deng ◽  
Renfang Wu
Keyword(s):  
Topological Index ◽  
Bipartite Graphs ◽  
Topological Indices ◽  
Extremal Graphs ◽  
Extremal Values

Let I(G) be a topological index of a graph. If I(G + e) < I(G) (or I(G + e) > I(G), respectively) for each edge e ? G, then I(G) is decreasing (or increasing, respectively) with addition of edges. In this paper, we determine the extremal values of some monotonic topological indices which decrease or increase with addition of edges, and characterize the corresponding extremal graphs among bipartite graphs with a given connectivity.

Vertex-degree-based topological indices of catacondensed hexagonal systems

2013 ◽  
Vol 572 ◽  
pp. 154-157 ◽  
Author(s):  
Juan Rada ◽  
Roberto Cruz ◽  
Ivan Gutman
Keyword(s):  
Topological Indices ◽  
Vertex Degree ◽  
Hexagonal Systems

On extremal bipartite graphs with given number of cut edges

2020 ◽  
Vol 12 (02) ◽  
pp. 2050015
Author(s):  
Hanlin Chen ◽  
Renfang Wu
Keyword(s):  
Topological Index ◽  
Wiener Index ◽  
Bipartite Graphs ◽  
Topological Indices ◽  
Extremal Graphs ◽  
Unified Approach ◽  
Harary Index ◽  
Eccentricity Index ◽  
Extremal Values

Let [Formula: see text] be a topological index of a graph. If [Formula: see text] (or [Formula: see text], respectively) for each edge [Formula: see text], then [Formula: see text] is monotonically decreasing (or increasing, respectively) with the addition of edges. In this paper, by a unified approach, we determine the extremal values of some monotonic topological indices, including the Wiener index, the hyper-Wiener index, the Harary index, the connective eccentricity index, the eccentricity distance sum, among all connected bipartite graphs with a given number of cut edges, and characterize the corresponding extremal graphs, respectively.

Extremal values of vertex-degree-based topological indices over graphs

2014 ◽  
Vol 48 (1-2) ◽  
pp. 395-406 ◽  
Author(s):  
Roberto Cruz ◽  
Tatiana Pérez ◽  
Juan Rada
Keyword(s):  
Topological Indices ◽  
Vertex Degree ◽  
Extremal Values

scholarly journals Computing Discrete Adriatic Indices of Probabilistic Neural Network

2020 ◽  
Vol 13 (5) ◽  
pp. 1149-1161
Author(s):  
T Deepika ◽  
V. Lokesha
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Topological Index ◽  
Probabilistic Neural Network ◽  
Topological Indices ◽  
Probabilistic Neural Networks ◽  
Mathematical Chemistry ◽  
International Academy

A Topological index is a numeric quantity which characterizes the whole structure of a graph. Adriatic indices are also part of topological indices, mainly it is classified into two namely extended variables and discrete adriatic indices, especially, discrete adriatic indices are analyzed on the testing sets provided by the International Academy of Mathematical Chemistry (IAMC) and it has been shown that they have good presaging substances in many compacts. This contrived attention to compute some discrete adriatic indices of probabilistic neural networks.

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