scholarly journals The rainbow vertex connection number of star wheel graphs

2019 ◽  
Author(s):  
Ariestha Widyastuty Bustan ◽  
A. N. M. Salman
Keyword(s):  
Connection Number ◽  
Wheel Graphs

A STUDY ON ZERO-M CORDIAL LABELING

2020 ◽  
Vol 9 (11) ◽  
pp. 9207-9218
Author(s):  
A. Neerajah ◽  
P. Subramanian
Keyword(s):  
Wheel Graphs

A labeling $f: E(G) \rightarrow \{1, -1\}$ of a graph G is called zero-M-cordial, if for each vertex v, the arithmetic sum of the labels occurrence with it is zero and $|e_{f}(-1) - e_{f}(1)| \leq 1$. A graph G is said to be Zero-M-cordial if a Zero-M-cordial label is given. Here the exploration of zero - M cordial labelings for deeds of paths, cycles, wheel and combining two wheel graphs, two Gear graphs, two Helm graphs. Here, also perceived that a zero-M-cordial labeling of a graph need not be a H-cordial labeling.

A Kind Of Conditional Vertex Connectivity Of Cayley Graphs Generated By Wheel Graphs

2019 ◽  
Vol 63 (9) ◽  
pp. 1372-1384
Author(s):  
Zuwen Luo ◽  
Liqiong Xu
Keyword(s):  
Fault Tolerance ◽  
Connected Graph ◽  
Cayley Graphs ◽  
Network Structures ◽  
Vertex Connectivity ◽  
Wheel Graphs

Abstract Let $G=(V(G), E(G))$ be a connected graph. A subset $T \subseteq V(G)$ is called an $R^{k}$-vertex-cut, if $G-T$ is disconnected and each vertex in $V(G)-T$ has at least $k$ neighbors in $G-T$. The cardinality of a minimum $R^{k}$-vertex-cut is the $R^{k}$-vertex-connectivity of $G$ and is denoted by $\kappa ^{k}(G)$. $R^{k}$-vertex-connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study $R^{1}$-vertex-connectivity and $R^{2}$-vertex-connectivity of Cayley graphs generated by wheel graphs, which are denoted by $AW_{n}$, and show that $\kappa ^{1}(AW_{n})=4n-7$ for $n\geq 6$; $\kappa ^{2}(AW_{n})=6n-12$ for $n\geq 6$.

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
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