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

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 Chromatic Number for a Generalization of Cartesian Product Graphs

10.37236/160 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Daniel Král' ◽  
Douglas B. West
Keyword(s):  
Chromatic Number ◽  
Maximum Degree ◽  
Cartesian Product ◽  
Rectangular Grid ◽  
Product Graphs ◽  
Cartesian Product Graphs

Let ${\cal G}$ be a class of graphs. A $d$-fold grid over ${\cal G}$ is a graph obtained from a $d$-dimensional rectangular grid of vertices by placing a graph from ${\cal G}$ on each of the lines parallel to one of the axes. Thus each vertex belongs to $d$ of these subgraphs. The class of $d$-fold grids over ${\cal G}$ is denoted by ${\cal G}^d$. Let $f({\cal G};d)=\max_{G\in{\cal G}^d}\chi(G)$. If each graph in ${\cal G}$ is $k$-colorable, then $f({\cal G};d)\le k^d$. We show that this bound is best possible by proving that $f({\cal G};d)=k^d$ when ${\cal G}$ is the class of all $k$-colorable graphs. We also show that $f({\cal G};d)\ge{\left\lfloor\sqrt{{d\over 6\log d}}\right\rfloor}$ when ${\cal G}$ is the class of graphs with at most one edge, and $f({\cal G};d)\ge {\left\lfloor{d\over 6\log d}\right\rfloor}$ when ${\cal G}$ is the class of graphs with maximum degree $1$.

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

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
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