Extremal values of vertex-degree-based topological indices over hexagonal systems with fixed number of vertices

2014 ◽  
Vol 243 ◽  
pp. 176-183 ◽  
Author(s):  
Lilia Berrocal ◽  
Aurora Olivieri ◽  
Juan Rada
Keyword(s):  
Fixed Number ◽  
Topological Indices ◽  
Vertex Degree ◽  
Extremal Values ◽  
Hexagonal Systems

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.

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

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 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.

Extremal Values of the Basic Invariants of Plane Curves

2000 ◽  
Vol 09 (08) ◽  
pp. 1085-1126
Author(s):  
Jianming Yu ◽  
Jianyi Zhou ◽  
Jianzhong Pan
Keyword(s):  
Fixed Number ◽  
Plane Curves ◽  
Explicit Formulas ◽  
Double Points ◽  
Fine Structures ◽  
Extremal Values ◽  
Extremal Value

In [A2] V.I. Arnold introduced three basic invariants St, J+ and J- of plane curves and proposed some interesting conjectures concerning the extremal value of these invariants on a given set of curves. Partial answers have been obtained by O. Viro and A. N. Shumakovich. We give explicit formulas for these extremal values of sets of plane curves with fixed number of double points and of Whitney index and we determine on which curves these extremal values are attained (Theorems 3-6). Our arguments are based on understanding of the fine structures of generic curves and some surgery operations on curves.

Sign in / Sign up

Export Citation Format

Share Document