scholarly journals On the independence number of minimum distance graphs

1998 ◽  
Vol 20 (2) ◽  
pp. 179-187 ◽  
Author(s):  
G. Csizmadia
Keyword(s):  
Minimum Distance ◽  
Independence Number ◽  
Distance Graphs

scholarly journals Hamiltonicity of Minimum Distance Graphs of 1-Perfect Codes

10.37236/2158 ◽  
2012 ◽  
Vol 19 (1) ◽  
Author(s):  
Alexander Mikhailovich Romanov
Keyword(s):  
Minimum Distance ◽  
Hamiltonian Cycle ◽  
Distance Graph ◽  
Perfect Code ◽  
Perfect Codes ◽  
Distance Graphs

A 1-perfect code $\mathcal{C}_{q}^{n}$ is called Hamiltonian if its minimum distance graph $G(\mathcal{C}_{q}^{n})$ contains a Hamiltonian cycle. In this paper, for  all admissible lengths $n \geq 13$, we construct   Hamiltonian nonlinear ternary 1-perfect  codes,   and for  all admissible lengths $n \geq 21$, we construct  Hamiltonian nonlinear quaternary 1-perfect  codes. The existence of Hamiltonian nonlinear $q$-ary 1-perfect  codes of length $N = qn + 1$ is reduced to the question of the existence of such codes of length $n$. Consequently,  for   $q = p^r$, where $p$ is prime, $r \geq 1$ there exist Hamiltonian nonlinear $q$-ary 1-perfect  codes of length $n = (q ^{m} -1) / (q-1)$, $m \geq 2$. If $q =2, 3, 4$, then $ m \neq 2$.  If $q =2$, then $ m \neq 3$.

On the independence number of distance graphs with vertices in {−1, 0, 1} n

2009 ◽  
Vol 86 (5-6) ◽  
pp. 744-746 ◽  
Author(s):  
A. É. Guterman ◽  
V. K. Lyubimov ◽  
A. M. Raigorodskii ◽  
S. A. Usachev
Keyword(s):  
Independence Number ◽  
Distance Graphs

scholarly journals On graphs with minimal distance signless Laplacian energy

2021 ◽  
Vol 13 (2) ◽  
pp. 450-467
Author(s):  
S. Pirzada ◽  
Bilal A. Rather ◽  
Rezwan Ul Shaban ◽  
Merajuddin
Keyword(s):  
Minimum Distance ◽  
Independence Number ◽  
Minimal Distance ◽  
Vertex Connectivity ◽  
Split Graph ◽  
Connected Graphs ◽  
Laplacian Eigenvalues ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Simple Connected Graph

Abstract For a simple connected graph G of order n having distance signless Laplacian eigenvalues ρ 1 Q ≥ ρ 2 Q ≥ ⋯ ≥ ρ n Q \rho _1^Q \ge \rho _2^Q \ge \cdots \ge \rho _n^Q , the distance signless Laplacian energy DSLE(G) is defined as D S L E ( G ) = ∑ i = 1 n | ρ i Q - 2 W ( G ) n | DSLE\left( G \right) = \sum\nolimits_{i = 1}^n {\left| {\rho _i^Q - {{2W\left( G \right)} \over n}} \right|} where W(G) is the Weiner index of G. We show that the complete split graph has the minimum distance signless Laplacian energy among all connected graphs with given independence number. Further, we prove that the graph Kk ∨ ( Kt∪ Kn−k−t), 1 ≤ t ≤ ⌊ n - k 2 ⌋ 1 \le t \le \left\lfloor {{{n - k} \over 2}} \right\rfloor has the minimum distance signless Laplacian energy among all connected graphs with vertex connectivity k.

scholarly journals Reconstructing Extended Perfect Binary One-Error-Correcting Codes From Their Minimum Distance Graphs

2009 ◽  
Vol 55 (6) ◽  
pp. 2622-2625 ◽  
Author(s):  
Ivan Yu. Mogilnykh ◽  
Patric R. J. Ostergard ◽  
Olli Pottonen ◽  
Faina I. Solov'eva
Keyword(s):  
Minimum Distance ◽  
Error Correcting Codes ◽  
Distance Graphs

A robust alignment-free fingerprint hashing algorithm based on minimum distance graphs

2012 ◽  
Vol 45 (9) ◽  
pp. 3373-3388 ◽  
Author(s):  
Priyanka Das ◽  
Kannan Karthik ◽  
Boul Chandra Garai
Keyword(s):  
Minimum Distance ◽  
Distance Graphs ◽  
Alignment Free ◽  
Hashing Algorithm

scholarly journals On the independence number of distance graphs with vertices in {-1, 0, 1}n

2019 ◽  
Vol 488 (5) ◽  
pp. 486-487 ◽  
Author(s):  
A. M. Raigorodskii ◽  
E. D. Shishunov
Keyword(s):  
Independence Number ◽  
Distance Graphs ◽  
Independence Numbers

In this work we find new bounds for the independence numbers of distance graphs with vertices in {-1, 0, 1}n.

Determining The Minimum Distance Between Centers of Two Parallel Tunnels to Apply The Law of Super Position in Order to Calculate Subsidence by Using The Software FLAC 3D

2015 ◽  
Vol 1 (1) ◽  
pp. 13-20
Author(s):  
Hamid Reza Samadi ◽  
Mohammad Reza Samadi
Keyword(s):  
Minimum Distance ◽  
Surface Subsidence ◽  
Urban Traffic ◽  
Underground Structures ◽  
Rapid Population Growth ◽  
The North ◽  
Flac 3D ◽  
The Law ◽  
3D Software ◽  
Twin Tunnels

Due to the development of cities as well as rapid population growth, urban traffic is increasing nowadays. Hence, to improve traffic flow, underground structures such as metro, especially in metropolises, are inevitable. This paper is a research on the twin tunnels Of Isfahan's metro between Shariaty station and Azadi station from the North towards the South. In this study, simultaneous drilling of subway's twin tunnels is simulated by means of Finite Difference Method (FDM) and FLAC 3D software. Moreover, the lowest distance between two tunnels is determined in a way that the Law of Super Position could be utilized to manually calculate the amount of surface subsidence, resulted by drilling two tunnels, by employing the results of the analysis of single tunnels without using simultaneous examination and simulation. In this paper, this distance is called "effective distance". For this purpose, first, the optimum dimensions of the model is chosen and then, five models with optimum dimensions will be analyzed separately, each of which in three steps. The results of analyses shows that the proportions (L/D) greater than or equal 2.80, the Law of Super Position can be applied for prediction of surface subsidence, caused by twin tunnels' construction

New Results on Edge Rotation Distance Graphs

2016 ◽  
Vol 6 (1) ◽  
pp. 81
Author(s):  
Medha Itagi Huilgol ◽  
Chitra Ramprakash
Keyword(s):  
Distance Graphs

Valued Field Graph and Some Related Parameters

2020 ◽  
pp. 389-395
Author(s):  
G. Suresh Singh ◽  
P. K. Prasobha
Keyword(s):  
Finite Field ◽  
Independence Number ◽  
Valued Field ◽  
Vertex Set ◽  
Adic Valuation

Let $K$ be any finite field. For any prime $p$, the $p$-adic valuation map is given by $\psi_{p}:K/\{0\} \to \R^+\bigcup\{0\}$ is given by $\psi_{p}(r) = n$ where $r = p^n \frac{a}{b}$, where $p,a,b$ are relatively prime. The field $K$ together with a valuation is called valued field. Also, any field $K$ has the trivial valuation determined by $\psi{(K)} = \{0,1\}$. Through out the paper K represents $\Z_q$. In this paper, we construct the graph corresponding to the valuation map called the valued field graph, denoted by $VFG_{p}(\Z_{q})$ whose vertex set is $\{v_0,v_1,v_2,\ldots, v_{q-1}\}$ where two vertices $v_i$ and $v_j$ are adjacent if $\psi_{p}(i) = j$ or $\psi_{p}(j) = i$. Here, we tried to characterize the valued field graph in $\Z_q$. Also we analyse various graph theoretical parameters such as diameter, independence number etc.

ENSURING THE PEDESTRIAN’S SAFETY DESIGN OF URBAN STREET CROSSWALKS

2019 ◽  
pp. 103-110
Author(s):  
Dmitriy Nemchinov
Keyword(s):  
Traffic Flow ◽  
Minimum Distance ◽  
Travel Speed ◽  
Vehicle Speed ◽  
Urban Street ◽  
Safety Design ◽  
Positive Practices ◽  
Time Required ◽  
Pedestrian Crossing ◽  
The City

The article presents an analysis of positive practices for ensuring the safety of pedestrians at the inter-section of the city streets carriageway, as well as a description of some innovations of regulatory and tech-nical documents, including an increased number of cases when a safety island can be arranged at a pedestri-an crossing. requirements for providing visibility at a pedestrian crossing to determine the minimum distance of visibility at a pedestrian crossing based on the time required pedestrians for crossing the roadway, recommended options for using ground unregulated pedestrian crossings on trapezoidal artificial irregularities according to GOST R 52605; traffic flow) and Z-shaped (also in the direction of the traffic flow), the requirements for the size of the securi-ty island have been established to allow put bicycle inside of safety island, a recommended set of measures to reduce the vehicle speed and describes the types of activities and describes a method of their application, describes methods zones device with reduced travel speed - residential and school zones, set requirements for turboroundabouts and methods of their design.

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