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

Packing Chromatic Number of Cycle Related Graphs

2014 ◽  
Vol 4 (1) ◽  
pp. 27
Author(s):  
Albert William ◽  
Roy Santiago ◽  
Indra Rajasingh
Keyword(s):  
Chromatic Number ◽  
Packing Chromatic Number

Packing coloring on subdivision-vertex and subdivision-edge join of cycle Cm with path Pn

2020 ◽  
pp. 627-634
Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik
Keyword(s):  
Chromatic Number ◽  
Path Graph ◽  
Packing Chromatic Number ◽  
Cycle Graph

The packing chromatic number $\chi_\rho$ of a graph $G$ is the smallest integer $k$ for which there exists a mapping $\pi$ from $V(G)$ to $\{1,2,...,k\}$ such that any two vertices of color $i$ are at distance at least $i+1$. In this paper, the authors find the packing chromatic number of subdivision vertex join of cycle graph with path graph and subdivision edge join of cycle graph with path graph.

scholarly journals The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs

2021 ◽  
Vol 33 (5) ◽  
pp. 66-73
Author(s):  
B. CHALUVARAJU ◽  
◽  
M. KUMARA ◽  
Keyword(s):  
Chromatic Number ◽  
Pairwise Distance ◽  
Circulant Graphs ◽  
Vertex Set ◽  
Packing Chromatic Number ◽  
Jump Sizes

The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,...,Vk , where vertices in Vi have pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}

scholarly journals Packing chromatic number of cubic graphs

2018 ◽  
Vol 341 (2) ◽  
pp. 474-483 ◽  
Author(s):  
József Balogh ◽  
Alexandr Kostochka ◽  
Xujun Liu
Keyword(s):  
Chromatic Number ◽  
Cubic Graphs ◽  
Packing Chromatic Number

Packing Chromatic Number of Base-3 Sierpiński Graphs

2015 ◽  
Vol 32 (4) ◽  
pp. 1313-1327 ◽  
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Douglas F. Rall
Keyword(s):  
Chromatic Number ◽  
Sierpiński Graphs ◽  
Packing Chromatic Number

scholarly journals On the packing chromatic number of Moore graphs

2021 ◽  
Vol 289 ◽  
pp. 185-193
Author(s):  
J. Fresán-Figueroa ◽  
D. González-Moreno ◽  
M. Olsen
Keyword(s):  
Chromatic Number ◽  
Packing Chromatic Number

scholarly journals The packing chromatic number of infinite product graphs

2009 ◽  
Vol 30 (5) ◽  
pp. 1101-1113 ◽  
Author(s):  
Jiří Fiala ◽  
Sandi Klavžar ◽  
Bernard Lidický
Keyword(s):  
Chromatic Number ◽  
Infinite Product ◽  
Product Graphs ◽  
Packing Chromatic Number

scholarly journals Packing chromatic number of transformation graphs

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1991-1995
Author(s):  
Derya Durgun ◽  
Busra Ozen-Dortok
Keyword(s):  
Chromatic Number ◽  
Graph Coloring ◽  
Chromatic Numbers ◽  
Np Complete ◽  
Packing Chromatic Number ◽  
General Graphs

Graph coloring is an assignment of labels called colors to elements of a graph. The packing coloring was introduced by Goddard et al. [1] in 2008 which is a kind of coloring of a graph. This problem is NP-complete for general graphs. In this paper, we consider some transformation graphs and generalized their packing chromatic numbers.

scholarly journals Packing chromatic numbers of finite super subdivisions of graphs

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3275-3286
Author(s):  
Rachid Lemdani ◽  
Moncef Abbas ◽  
Jasmina Ferme
Keyword(s):  
Positive Integer ◽  
Chromatic Number ◽  
Complete Graphs ◽  
Chromatic Numbers ◽  
General Properties ◽  
Vertex Set ◽  
Packing Chromatic Number ◽  
Corona Graphs

Given a graph G and a positive integer i, an i-packing in G is a subset W of the vertex set of G such that the distance between any two distinct vertices from W is greater than i. The packing chromatic number of a graph G, ??(G), is the smallest integer k such that the vertex set of G can be partitioned into sets Vi, i ? {1,..., k}, where each Vi is an i-packing. In this paper, we present some general properties of packing chromatic numbers of finite super subdivisions of graphs. We determine the packing chromatic numbers of the finite super subdivisions of complete graphs, cycles and some neighborhood corona graphs.

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