scholarly journals Conflict-free vertex connection number at most 3 and size of graphs

2021 ◽  
Vol 41 (2) ◽  
pp. 617 ◽  
Author(s):  
Trung Duy Doan ◽  
Ingo Schiermeyer
Keyword(s):  
Connection Number ◽  
Free Vertex

Maximum value of conflict-free vertex-connection number of graphs

2018 ◽  
Vol 10 (05) ◽  
pp. 1850059 ◽  
Author(s):  
Zhenzhen Li ◽  
Baoyindureng Wu
Keyword(s):  
Free Path ◽  
Connected Graph ◽  
Colored Graph ◽  
Connection Number ◽  
Free Vertex ◽  
Maximum Value

A path in a vertex-colored graph is called conflict-free if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be conflict-free vertex-connected if any two vertices of the graph are connected by a conflict-free path. The conflict-free vertex-connection number, denoted by [Formula: see text], is defined as the smallest number of colors required to make [Formula: see text] conflict-free vertex-connected. Li et al. [Conflict-free vertex-connections of graphs, preprint (2017), arXiv:1705.07270v1[math.CO]] conjectured that for a connected graph [Formula: see text] of order [Formula: see text], [Formula: see text]. We confirm that the conjecture is true and poses two relevant conjectures.

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
Sign in / Sign up

Export Citation Format

Share Document