scholarly journals Degree Sequence of Graph Operator for some Standard Graphs

2020 ◽  
Vol 5 (2) ◽  
pp. 99-108
Author(s):  
◽  
P. S Ranjini ◽  
V. Lokesha ◽  
Sandeep Kumar
Keyword(s):  
Degree Sequence ◽  
Topological Indices ◽  
Vertex Degree ◽  
Mathematical Chemistry

AbstractTopological indices play a very important role in the mathematical chemistry. The topological indices are numerical parameters of a graph. The degree sequence is obtained by considering the set of vertex degree of a graph. Graph operators are the ones which are used to obtain another broader graphs. This paper attempts to find degree sequence of vertex–F join operation of graphs for some standard graphs.

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.

scholarly journals On relations between Kirchhoff index, Laplacian energy, Laplacian-energy-like invariant and degree deviation of graphs

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 1025-1033
Author(s):  
Predrag Milosevic ◽  
Emina Milovanovic ◽  
Marjan Matejic ◽  
Igor Milovanovic
Keyword(s):  
Topological Index ◽  
Degree Sequence ◽  
Laplacian Matrix ◽  
Vertex Degree ◽  
Graph Invariants ◽  
Kirchhoff Index ◽  
Laplacian Eigenvalues ◽  
Laplacian Energy ◽  
Degree Deviation ◽  
Simple Connected Graph

Let G be a simple connected graph of order n and size m, vertex degree sequence d1 ? d2 ?...? dn > 0, and let ?1 ? ? 2 ? ... ? ?n-1 > ?n = 0 be the eigenvalues of its Laplacian matrix. Laplacian energy LE, Laplacian-energy-like invariant LEL and Kirchhoff index Kf, are graph invariants defined in terms of Laplacian eigenvalues. These are, respectively, defined as LE(G) = ?n,i=1 |?i-2m/n|, LEL(G) = ?n-1 i=1 ??i and Kf (G) = n ?n-1,i=1 1/?i. A vertex-degree-based topological index referred to as degree deviation is defined as S(G) = ?n,i=1 |di- 2m/n|. Relations between Kf and LE, Kf and LEL, as well as Kf and S are obtained.

scholarly journals A note on the edge reconstruction conjecture

1975 ◽  
Vol 12 (1) ◽  
pp. 27-30 ◽  
Author(s):  
E.F. Schmeichel
Keyword(s):  
Degree Sequence ◽  
Existence Condition ◽  
Vertex Degree ◽  
Hamiltonian Cycles ◽  
Edge Reconstruction

Let G be a graph with vertex degree sequence d1 ≤ d2 ≤ … ≤ dp It is shown that if di + dp–i+1 ≥ p for some i, then G is uniquely reconstructable from its collection of maximal (edge deleted) subgraphs. This generalizes considerably a result of Lovász. As a corollary, it is shown that Chvátal's existence condition for hamiltonian cycles implies edge reconstructability as well.

A Small-World Model of Scale-Free Networks: Features and Verifications

2011 ◽  
Vol 50-51 ◽  
pp. 166-170 ◽  
Author(s):  
Wen Jun Xiao ◽  
Shi Zhong Jiang ◽  
Guan Rong Chen
Keyword(s):  
Complex Networks ◽  
Power Law ◽  
Degree Sequence ◽  
Small World ◽  
Static Condition ◽  
Vertex Degree ◽  
Power Law Distribution ◽  
Least Common Multiple ◽  
Scale Free ◽  
Vertex Degrees

It is now well known that many large-sized complex networks obey a scale-free power-law vertex-degree distribution. Here, we show that when the vertex degrees of a large-sized network follow a scale-free power-law distribution with exponent  2, the number of degree-1 vertices, if nonzero, is of order N and the average degree is of order lower than log N, where N is the size of the network. Furthermore, we show that the number of degree-1 vertices is divisible by the least common multiple of , , . . ., , and l is less than log N, where l = < is the vertex-degree sequence of the network. The method we developed here relies only on a static condition, which can be easily verified, and we have verified it by a large number of real complex networks.

scholarly journals Vertex-degree-based topological indices over starlike trees

2015 ◽  
Vol 185 ◽  
pp. 18-25 ◽  
Author(s):  
Clara Betancur ◽  
Roberto Cruz ◽  
Juan Rada
Keyword(s):  
Topological Indices ◽  
Vertex Degree

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 Four vertex degree topological indices of tri-hexagonal boron nanotube and nanotori

2019 ◽  
Author(s):  
Roshini Gujar Ravichandra ◽  
Chandrakala Sogenahalli Boraiah ◽  
Sooryanarayana Badekara
Keyword(s):  
Topological Indices ◽  
Vertex Degree ◽  
Boron Nanotube
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