A study on harmonious chromatic number of total graph of central graph of generalized Petersen graph

2020 ◽  
Author(s):  
M. S. Franklin Thamil Selvi ◽  
A. Amutha
Keyword(s):  
Chromatic Number ◽  
Petersen Graph ◽  
Total Graph ◽  
Generalized Petersen Graph

scholarly journals PEWARNAAN TITIK TOTAL SUPER ANTI-AJAIB LOKAL PADA GRAF PETERSEN DIPERUMUM P(n,k) DENGAN k=1,2

2021 ◽  
Vol 15 (4) ◽  
pp. 651-658
Author(s):  
Deddy Setyawan ◽  
Anis Nur Afni ◽  
Rafiantika Megahnia Prihandini ◽  
Ermita Rizki Albirri ◽  
Arika Indah Kristiana
Keyword(s):  
Natural Number ◽  
Chromatic Number ◽  
Petersen Graph ◽  
Vertex Coloring ◽  
Generalized Petersen Graph ◽  
Minimum Number ◽  
Vertex Label

The local antimagic total vertex labeling of graph G is a labeling that every vertices and edges label by natural number from 1 to  such that every two adjacent vertices has different weights, where is The sum of a vertex label and the labels of all edges that incident to the vertex. If the labeling start the smallest label from the vertex  then the edge  so that kind of coloring is called the local super antimagic total vertex labeling. That local super antimagic total vertex labeling induces vertex coloring of graph G where for vertex v, the weight  w(v) is the color of  v. The minimum number of colors that obtained by coloring that induces by local super antimagic total vertex labeling of G called the chromatic number of local super antimagic total vertex coloring of G, denoted by χlsat(G). In this paper, we consider the chromatic number of local super antimagic total vertex coloring of Generalized Petersen Graph P(n,k) for k=1, 2.

The Generalized Connectivity of Generalized Petersen Graph

2021 ◽  
Author(s):  
Yuan Si ◽  
Ping Li ◽  
Yuzhi Xiao ◽  
Jinxia Liang
Keyword(s):  
Steiner Trees ◽  
Petersen Graph ◽  
Generalized Petersen Graph ◽  
Edge Disjoint ◽  
Generalized Connectivity ◽  
Vertex Set

For a vertex set [Formula: see text] of [Formula: see text], we use [Formula: see text] to denote the maximum number of edge-disjoint Steiner trees of [Formula: see text] such that any two of such trees intersect in [Formula: see text]. The generalized [Formula: see text]-connectivity of [Formula: see text] is defined as [Formula: see text]. We get that for any generalized Petersen graph [Formula: see text] with [Formula: see text], [Formula: see text] when [Formula: see text]. We give the values of [Formula: see text] for Petersen graph [Formula: see text], where [Formula: see text], and the values of [Formula: see text] for generalized Petersen graph [Formula: see text], where [Formula: see text] and [Formula: see text].

scholarly journals ON DYNAMIC COLORING OF WEB GRAPH

2018 ◽  
Vol 5 (2) ◽  
pp. 11-15
Author(s):  
Aaresh R.R ◽  
Venkatachalam M ◽  
Deepa T
Keyword(s):  
Chromatic Number ◽  
Line Graph ◽  
Proper Coloring ◽  
Total Graph ◽  
Web Graph ◽  
Middle Graph

Dynamic coloring of a graph G is a proper coloring. The chromatic number of a graph G is the minimum k such that G has a dynamic coloring with k colors. In this paper we investigate the dynamic chromatic number for the Central graph, Middle graph, Total graph and Line graph of Web graph Wn denoted by C(Wn), M(Wn), T(Wn) and L(Wn) respectively.

scholarly journals On r-dynamic coloring of comb graphs

2021 ◽  
Vol 27 (2) ◽  
pp. 191-200
Author(s):  
K. Kalaiselvi ◽  
◽  
N. Mohanapriya ◽  
J. Vernold Vivin ◽  
◽  
...  
Keyword(s):  
Lower Bound ◽  
Chromatic Number ◽  
Upper Bound ◽  
Line Graph ◽  
Proper Coloring ◽  
Total Graph ◽  
Middle Graph ◽  
Different Color

An r-dynamic coloring of a graph G is a proper coloring of G such that every vertex in V(G) has neighbors in at least $\min\{d(v),r\}$ different color classes. The r-dynamic chromatic number of graph G denoted as $\chi_r (G)$, is the least k such that G has a coloring. In this paper we obtain the r-dynamic chromatic number of the central graph, middle graph, total graph, line graph, para-line graph and sub-division graph of the comb graph $P_n\odot K_1$ denoted by $C(P_n\odot K_1), M(P_n\odot K_1), T(P_n\odot K_1), L(P_n\odot K_1), P(P_n\odot K_1)$ and $S(P_n\odot K_1)$ respectively by finding the upper bound and lower bound for the r-dynamic chromatic number of the Comb graph.

scholarly journals The K -Size Edge Metric Dimension of Graphs

2020 ◽  
Vol 2020 ◽  
pp. 1-7
Author(s):  
Tanveer Iqbal ◽  
Muhammad Naeem Azhar ◽  
Syed Ahtsham Ul Haq Bokhary
Keyword(s):  
Bipartite Graph ◽  
Connected Graph ◽  
Complete Bipartite Graph ◽  
Petersen Graph ◽  
Metric Dimension ◽  
Resolving Set ◽  
Generalized Petersen Graph

In this paper, a new concept k -size edge resolving set for a connected graph G in the context of resolvability of graphs is defined. Some properties and realizable results on k -size edge resolvability of graphs are studied. The existence of this new parameter in different graphs is investigated, and the k -size edge metric dimension of path, cycle, and complete bipartite graph is computed. It is shown that these families have unbounded k -size edge metric dimension. Furthermore, the k-size edge metric dimension of the graphs Pm □ Pn, Pm □ Cn for m, n ≥ 3 and the generalized Petersen graph is determined. It is shown that these families of graphs have constant k -size edge metric dimension.

Packing chromatic number, $$\mathbf (1, 1, 2, 2) $$ ( 1 , 1 , 2 , 2 ) -colorings, and characterizing the Petersen graph

2017 ◽  
Vol 91 (1) ◽  
pp. 169-184 ◽  
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Douglas F. Rall ◽  
Kirsti Wash
Keyword(s):  
Chromatic Number ◽  
Petersen Graph ◽  
Packing Chromatic Number

Total irregularity strength of disjoint union of isomorphic copies of generalized Petersen graph

2017 ◽  
Vol 09 (06) ◽  
pp. 1750071
Author(s):  
Muhammad Naeem ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Disjoint Union ◽  
Petersen Graph ◽  
Generalized Petersen Graph ◽  
Irregularity Strength

Let [Formula: see text] be a graph. A total labeling [Formula: see text] is called totally irregular total [Formula: see text]-labeling of [Formula: see text] if every two distinct vertices [Formula: see text] and [Formula: see text] in [Formula: see text] satisfy [Formula: see text] and every two distinct edges [Formula: see text] and [Formula: see text] in [Formula: see text] satisfy [Formula: see text] where [Formula: see text] and [Formula: see text] The minimum [Formula: see text] for which a graph [Formula: see text] has a totally irregular total [Formula: see text]-labeling is called the total irregularity strength of [Formula: see text], denoted by [Formula: see text] In this paper, we determined the total irregularity strength of disjoint union of [Formula: see text] isomorphic copies of generalized Petersen graph.

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