Modeling Boiling Points of Cycloalkanes by Means of Iterated Line Graph Sequences

2001 ◽  
Vol 41 (4) ◽  
pp. 1041-1045 ◽  
Author(s):  
Željko Tomović ◽  
Ivan Gutman
Keyword(s):  
Line Graph ◽  
Iterated Line Graph ◽  
Boiling Points

ChemInform Abstract: Modeling Boiling Points of Cycloalkanes by Means of Iterated Line Graph Sequences.

ChemInform ◽  
2010 ◽  
Vol 32 (45) ◽  
pp. no-no
Author(s):  
Zeljko Tomovic ◽  
Ivan Gutman
Keyword(s):  
Line Graph ◽  
Iterated Line Graph ◽  
Boiling Points

scholarly journals Nonplanarity of Iterated Line Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Jing Wang
Keyword(s):  
Line Graph ◽  
Crossing Number ◽  
Line Graphs ◽  
Full Characterization ◽  
Iterated Line Graph

The 1-crossing index of a graph G is the smallest integer k such that the k th iterated line graph of G has crossing number greater than 1. In this paper, we show that the 1-crossing index of a graph is either infinite or it is at most 5. Moreover, we give a full characterization of all graphs with respect to their 1-crossing index.

scholarly journals Maximum Degree Growth of the Iterated Line Graph

10.37236/1460 ◽  
1999 ◽  
Vol 6 (1) ◽  
Author(s):  
Stephen G. Hartke ◽  
Aparna W. Higgins
Keyword(s):  
Connected Graph ◽  
Maximum Degree ◽  
Line Graph ◽  
Induced Subgraphs ◽  
Iterated Line Graph

Let $\Delta_k$ denote the maximum degree of the $k^{\rm th}$ iterated line graph $L^k(G)$. For any connected graph $G$ that is not a path, the inequality $\Delta_{k+1}\leq 2\Delta_k-2$ holds. Niepel, Knor, and Šoltés have conjectured that there exists an integer $K$ such that, for all $k\geq K$, equality holds; that is, the maximum degree $\Delta_k$ attains the greatest possible growth. We prove this conjecture using induced subgraphs of maximum degree vertices and locally maximum vertices.

scholarly journals Trees T satisfying W(L3(T))= W(T)

Filomat ◽  
2014 ◽  
Vol 28 (3) ◽  
pp. 551-556 ◽  
Author(s):  
Martin Knor ◽  
Martin Macaj ◽  
Primoz Potocnik ◽  
Riste Skrekovski
Keyword(s):  
Line Graph ◽  
Wiener Index ◽  
Discrete Math ◽  
Infinite Class ◽  
Iterated Line Graph

Let G be a graph. Denote by Li(G) its i-iterated line graph and denote by W(G) its Wiener index. We find an infinite class of trees T satisfying W(L3(T)) = W(T), which disproves a conjecture of Dobrynin and Entringer [Electronic Notes in Discrete Math. 22 (2005) 469-475].

scholarly journals Distance spectra and distance energies of iterated line graphs of regular graphs

2009 ◽  
Vol 85 (99) ◽  
pp. 39-46 ◽  
Author(s):  
H.S. Ramane ◽  
D.S. Revankar ◽  
Ivan Gutman ◽  
H.B. Walikar
Keyword(s):  
Line Graph ◽  
Distance Matrix ◽  
Line Graphs ◽  
Regular Graphs ◽  
Induced Subgraphs ◽  
Induced Subgraph ◽  
Iterated Line Graph ◽  
The Absolute ◽  
Equienergetic Graphs

The distance or D-eigenvalues of a graph G are the eigenvalues of its distance matrix. The distance or D-energy ED(G) of the graph G is the sum of the absolute values of its D-eigenvalues. Two graphs G1 and G2 are said to be D-equienergetic if ED(G1) = ED(G2). Let F1 be the 5-vertex path, F2 the graph obtained by identifying one vertex of a triangle with one end vertex of the 3-vertex path, F3 the graph obtained by identifying a vertex of a triangle with a vertex of another triangle and F4 be the graph obtained by identifying one end vertex of a 4-vertex star with a middle vertex of a 3-vertex path. In this paper we show that if G is r-regular, with diam(G)? 2, and Fi,i = 1,2,3,4, are not induced subgraphs of G, then the k-th iterated line graph Lk(G) has exactly one positive D-eigenvalue. Further, if G is r-regular, of order n, diam(G)?2, and G does not have Fi,i=1,2,3,4, as an induced subgraph, then for k ?1, ED(Lk(G)) depends solely on n and r. This result leads to the construction of non D-cospectral, D-equienergetic graphs having same number of vertices and same number of edges.

Gas-Cycle-Assisted Headspace Solid-Phase Microextraction Coupling with Gas Chromatography for Rapid Analysis of Organic Pollutants

2021 ◽  
Author(s):  
Wenli Zhu ◽  
Peige Qin ◽  
Lizhen Han ◽  
Xiaowan Zhang ◽  
Dan Li ◽  
...  
Keyword(s):  
Gas Chromatography ◽  
Organic Pollutants ◽  
Solid Phase Microextraction ◽  
Solid Phase ◽  
Rapid Analysis ◽  
Headspace Solid Phase Microextraction ◽  
Boiling Points

Herein, a new gas-cycle-assisted (GCA) headspace solid-phase microextraction (HS-SPME) device was designed to rapidly extract organic pollutants with high Kow and boiling points that have difficulty in volatilization from matrix...

scholarly journals Computing Topological Indices for Para-Line Graphs of Anthracene

2019 ◽  
Vol 17 (1) ◽  
pp. 955-962 ◽  
Author(s):  
Zhiqiang Zhang ◽  
Zeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Zaheer Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Line Graph ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Molar Refraction ◽  
Chromatographic Behavior ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

scholarly journals A graph-based algorithm for detecting rigid domains in protein structures

2021 ◽  
Vol 22 (1) ◽  
Author(s):  
Truong Khanh Linh Dang ◽  
Thach Nguyen ◽  
Michael Habeck ◽  
Mehmet Gültas ◽  
Stephan Waack
Keyword(s):  
Structural Changes ◽  
Viterbi Algorithm ◽  
Structural Information ◽  
Line Graph ◽  
Clustering Algorithms ◽  
Protein Structures ◽  
Alternative Methods ◽  
Structural Transitions ◽  
Tuning Parameters ◽  
Conformational Ensembles

Abstract Background Conformational transitions are implicated in the biological function of many proteins. Structural changes in proteins can be described approximately as the relative movement of rigid domains against each other. Despite previous efforts, there is a need to develop new domain segmentation algorithms that are capable of analysing the entire structure database efficiently and do not require the choice of protein-dependent tuning parameters such as the number of rigid domains. Results We develop a graph-based method for detecting rigid domains in proteins. Structural information from multiple conformational states is represented by a graph whose nodes correspond to amino acids. Graph clustering algorithms allow us to reduce the graph and run the Viterbi algorithm on the associated line graph to obtain a segmentation of the input structures into rigid domains. In contrast to many alternative methods, our approach does not require knowledge about the number of rigid domains. Moreover, we identified default values for the algorithmic parameters that are suitable for a large number of conformational ensembles. We test our algorithm on examples from the DynDom database and illustrate our method on various challenging systems whose structural transitions have been studied extensively. Conclusions The results strongly suggest that our graph-based algorithm forms a novel framework to characterize structural transitions in proteins via detecting their rigid domains. The web server is available at http://azifi.tz.agrar.uni-goettingen.de/webservice/.

scholarly journals A New Method for Type Synthesis of 2R1T and 2T1R 3-DOF Redundant Actuated Parallel Mechanisms with Closed Loop Units

2020 ◽  
Vol 33 (1) ◽  
Author(s):  
Yongquan Li ◽  
Yang Zhang ◽  
Lijie Zhang
Keyword(s):  
Closed Loop ◽  
Screw Theory ◽  
Line Graph ◽  
Degree Of Freedom ◽  
Parallel Mechanisms ◽  
Type Synthesis ◽  
Allocation Criteria ◽  
Grassmann Line Geometry ◽  
Moving Platform ◽  
Atlas Method

Abstract The current type synthesis of the redundant actuated parallel mechanisms is adding active-actuated kinematic branches on the basis of the traditional parallel mechanisms, or using screw theory to perform multiple getting intersection and union to complete type synthesis. The number of redundant parallel mechanisms obtained by these two methods is limited. In this paper, based on Grassmann line geometry and Atlas method, a novel and effective method for type synthesis of redundant actuated parallel mechanisms (PMs) with closed-loop units is proposed. Firstly, the degree of freedom (DOF) and constraint line graph of the moving platform are determined successively, and redundant lines are added in constraint line graph to obtain the redundant constraint line graph and their equivalent line graph, and a branch constraint allocation scheme is formulated based on the allocation criteria. Secondly, a scheme is selected and redundant lines are added in the branch chains DOF graph to construct the redundant actuated branch chains with closed-loop units. Finally, the branch chains that meet the requirements of branch chains configuration criteria and F&C (degree of freedom & constraint) line graph are assembled. In this paper, two types of 2 rotational and 1 translational (2R1T) redundant actuated parallel mechanisms and one type of 2 translational and 1 rotational (2T1R) redundant actuated parallel mechanisms with few branches and closed-loop units were taken as examples, and 238, 92 and 15 new configurations were synthesized. All the mechanisms contain closed-loop units, and the mechanisms and the actuators both have good symmetry. Therefore, all the mechanisms have excellent comprehensive performance, in which the two rotational DOFs of the moving platform of 2R1T redundant actuated parallel mechanism can be independently controlled. The instantaneous analysis shows that all mechanisms are not instantaneous, which proves the feasibility and practicability of the method.

Sign in / Sign up

Export Citation Format

Share Document