On the packing chromatic number of vertex amalgamation of some related tree 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.

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The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs

Journal of Ultra Scientist of Physical Sciences Section A ◽

10.22147/jusps-a/330501 ◽

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._{}

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Packing chromatic number of cubic graphs

Discrete Mathematics ◽

10.1016/j.disc.2017.09.014 ◽

2018 ◽

Vol 341 (2) ◽

pp. 474-483 ◽

Cited By ~ 10

Author(s):

József Balogh ◽

Alexandr Kostochka ◽

Xujun Liu

Keyword(s):

Chromatic Number ◽

Cubic Graphs ◽

Packing Chromatic Number

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Packing Chromatic Number of Base-3 Sierpiński Graphs

Graphs and Combinatorics ◽

10.1007/s00373-015-1647-x ◽

2015 ◽

Vol 32 (4) ◽

pp. 1313-1327 ◽

Cited By ~ 14

Author(s):

Boštjan Brešar ◽

Sandi Klavžar ◽

Douglas F. Rall

Keyword(s):

Chromatic Number ◽

Sierpiński Graphs ◽

Packing Chromatic Number

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On the packing chromatic number of Moore graphs

Discrete Applied Mathematics ◽

10.1016/j.dam.2020.10.009 ◽

2021 ◽

Vol 289 ◽

pp. 185-193

Author(s):

J. Fresán-Figueroa ◽

D. González-Moreno ◽

M. Olsen

Keyword(s):

Chromatic Number ◽

Packing Chromatic Number

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

Aequationes Mathematicae ◽

10.1007/s00010-016-0461-8 ◽

2017 ◽

Vol 91 (1) ◽

pp. 169-184 ◽

Cited By ~ 10

Author(s):

Boštjan Brešar ◽

Sandi Klavžar ◽

Douglas F. Rall ◽

Kirsti Wash

Keyword(s):

Chromatic Number ◽

Petersen Graph ◽

Packing Chromatic Number

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The packing chromatic number of infinite product graphs

European Journal of Combinatorics ◽

10.1016/j.ejc.2008.09.014 ◽

2009 ◽

Vol 30 (5) ◽

pp. 1101-1113 ◽

Cited By ~ 26

Author(s):

Jiří Fiala ◽

Sandi Klavžar ◽

Bernard Lidický

Keyword(s):

Chromatic Number ◽

Infinite Product ◽

Product Graphs ◽

Packing Chromatic Number

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Packing chromatic number of transformation graphs

Thermal Science ◽

10.2298/tsci190720363d ◽

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.

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Packing chromatic numbers of finite super subdivisions of graphs

Filomat ◽

10.2298/fil2010275l ◽

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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