Rainbow vertex connection number of square, glue, middle and splitting graph of brush graph

2020 ◽  
Author(s):  
Helmi Helmi ◽  
Brella Glysentia Vilgalita ◽  
Fransiskus Fran ◽  
Dany Riansyah Putra
Keyword(s):  
Connection Number ◽  
Splitting Graph

Voltage Sag Evaluation Method of a Real Distribution System Based on a Connection Number Model

2013 ◽  
Vol 341-342 ◽  
pp. 1363-1366
Author(s):  
Lang Bai ◽  
Le Yu
Keyword(s):  
Distribution System ◽  
Evaluation Method ◽  
Assessment Model ◽  
Voltage Sag ◽  
Voltage Sags ◽  
Connection Number ◽  
Reliability Parameters ◽  
Real Distribution ◽  
System Components ◽  
Simulation Results

The evaluation results of power system are greatly influenced by the reliability parameters and uncertainty of system components. The connection number assessment model and an approach have been presented to assess the occurrence frequency due to voltage sags. The proposed method had been applied to a real distribution system. Compared with the interval number method, the simulation results have shown that this method is simple and flexible.

A NOTE ON GENERALIZED RAINBOW CONNECTION OF CONNECTED GRAPHS AND THEIR NUMBER OF EDGES

2021 ◽  
Vol 66 (3) ◽  
pp. 3-7
Author(s):  
Anh Nguyen Thi Thuy ◽  
Duyen Le Thi
Keyword(s):  
Upper Bound ◽  
Connected Graph ◽  
Connection Number ◽  
Connected Graphs ◽  
Rainbow Connection Number ◽  
Rainbow Connection ◽  
Rainbow Path ◽  
Vertex Disjoint

Let l ≥ 1, k ≥ 1 be two integers. Given an edge-coloured connected graph G. A path P in the graph G is called l-rainbow path if each subpath of length at most l + 1 is rainbow. The graph G is called (k, l)-rainbow connected if any two vertices in G are connected by at least k pairwise internally vertex-disjoint l-rainbow paths. The smallest number of colours needed in order to make G (k, l)-rainbow connected is called the (k, l)-rainbow connection number of G and denoted by rck,l(G). In this paper, we first focus to improve the upper bound of the (1, l)-rainbow connection number depending on the size of connected graphs. Using this result, we characterize all connected graphs having the large (1, 2)-rainbow connection number. Moreover, we also determine the (1, l)-rainbow connection number in a connected graph G containing a sequence of cut-edges.

A new condition for a graph having conflict free connection number 2

2021 ◽  
Vol 66 (1) ◽  
pp. 25-29
Author(s):  
Diep Pham Ngoc
Keyword(s):  
Free Path ◽  
Complete Graph ◽  
Connection Number

A path in an edge-coloured graph is called conflict-free if there is a colour used on exactly one of its edges. An edge-coloured graph is said to be conflict-free connected if any two distinct vertices of the graph are connected by a conflict-free path. The conflict-free connection number, denoted by cf c(G), is the smallest number of colours needed in order to make G conflict-free connected. In this paper, we give a new condition to show that a connected non-complete graph G having cf c(G) = 2. This is an extension of a result by Chang et al. [1].

scholarly journals Graphs with Conflict-Free Connection Number Two

2018 ◽  
Vol 34 (6) ◽  
pp. 1553-1563 ◽  
Author(s):  
Hong Chang ◽  
Trung Duy Doan ◽  
Zhong Huang ◽  
Stanislav Jendrol’ ◽  
Xueliang Li ◽  
...  
Keyword(s):  
Connection Number

Rainbow vertex-connection number of 3-connected graph

2017 ◽  
Vol 11 ◽  
pp. 751-757 ◽  
Author(s):  
Zhiping Wang ◽  
Yixiao Liu ◽  
Xiaojing Xu
Keyword(s):  
Connected Graph ◽  
Connection Number

scholarly journals PENENTUAN RAINBOW CONNECTION NUMBER UNTUK AMALGAMASI GRAF LENGKAP DENGAN GRAF RODA

2019 ◽  
Vol 8 (1) ◽  
pp. 345
Author(s):  
Risya Hazani Utari ◽  
Lyra Yulianti ◽  
Syafrizal Sy
Keyword(s):  
Connection Number ◽  
Rainbow Connection Number ◽  
Rainbow Connection

Suatu pewarnaan terhadap sisi-sisi di graf G terhubung tak trivial didefinisikan sebagai c : E(G) → {1, 2, · · · , k} untuk k ∈ N adalah suatu pewarnaan terhadap sisi-sisi di G sedemikian sehingga setiap sisi yang bertetangga boleh diberi warna yang sama. Banyaknya warna minimal yang diperlukan untuk membuat graf G bersifat rainbow connected disebut dengan rainbow connection number dari G, yang dinotasikan dengan rc(G). Penelitian ini menentukan rainbow connection number untuk amalgamasi 2 buah graf lengkap K4 dengan 2 buah graf roda W4 yang diperoleh dari menggabungkan satu titik pada setiap graf lengkap K4 dengan satu titik pusat pada setiap graf roda W4.Kata Kunci: Amalgamasi, Graf lengkap K4, Graf Roda W4, Rainbow Connection Number

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