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
Author(s):  
Albert William ◽  
Roy Santiago ◽  
Indra Rajasingh

Author(s):  
K. Rajalakshmi ◽  
M. Venkatachalam ◽  
M. Barani ◽  
D. Dafik

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.


2021 ◽  
Vol 33 (5) ◽  
pp. 66-73
Author(s):  
B. CHALUVARAJU ◽  
◽  
M. KUMARA ◽  

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._{}


2018 ◽  
Vol 341 (2) ◽  
pp. 474-483 ◽  
Author(s):  
József Balogh ◽  
Alexandr Kostochka ◽  
Xujun Liu

2015 ◽  
Vol 32 (4) ◽  
pp. 1313-1327 ◽  
Author(s):  
Boštjan Brešar ◽  
Sandi Klavžar ◽  
Douglas F. Rall

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

2009 ◽  
Vol 30 (5) ◽  
pp. 1101-1113 ◽  
Author(s):  
Jiří Fiala ◽  
Sandi Klavžar ◽  
Bernard Lidický

2019 ◽  
Vol 23 (Suppl. 6) ◽  
pp. 1991-1995
Author(s):  
Derya Durgun ◽  
Busra Ozen-Dortok

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.


Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3275-3286
Author(s):  
Rachid Lemdani ◽  
Moncef Abbas ◽  
Jasmina Ferme

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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