Temat: radio coloring - Katalog OPAC zbiorów

Skocz do pozycji: 1.

Tytuł:: Triameter of Graphs
Autorzy:: Das, Angsuman
Powiązania:: https://bibliotekanauki.pl/articles/32083897.pdf
Data publikacji:: 2021-05-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: distance
radio k -coloring
Nordhaus-Gaddum bounds
Opis:: In this paper, we study a new distance parameter triameter of a connected graph G, which is defined as max{d(u; v)+d(v;w)+d(u;w) : u; v;w ∈ V} and is denoted by tr(G). We find various upper and lower bounds on tr(G) in terms of order, girth, domination parameters etc., and characterize the graphs attaining those bounds. In the process, we provide some lower bounds of (connected, total) domination numbers of a connected graph in terms of its triameter. The lower bound on total domination number was proved earlier by Henning and Yeo. We provide a shorter proof of that. Moreover, we prove Nordhaus-Gaddum type bounds on tr(G) and find tr(G) for some specific family of graphs.
Źródło:: Discussiones Mathematicae Graph Theory; 2021, 41, 2; 601-616
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 2.

Tytuł:: Radio k-colorings of paths
Autorzy:: Chartrand, Gary
Nebeský, Ladislav
Zhang, Ping
Powiązania:: https://bibliotekanauki.pl/articles/743194.pdf
Data publikacji:: 2004
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: radio k-coloring
radio k-chromatic number
Opis:: For a connected graph G of diameter d and an integer k with 1 ≤ k ≤ d, a radio k-coloring of G is an assignment c of colors (positive integers) to the vertices of G such that
d(u,v) + |c(u)- c(v)| ≥ 1 + k
for every two distinct vertices u and v of G, where d(u,v) is the distance between u and v. The value rcₖ(c) of a radio k-coloring c of G is the maximum color assigned to a vertex of G. The radio k-chromatic number rcₖ(G) of G is the minimum value of rcₖ(c) taken over all radio k-colorings c of G. In this paper, radio k-colorings of paths are studied. For the path Pₙ of order n ≥ 9 and n odd, a new improved bound for $rc_{n- 2}(Pₙ)$ is presented. For n ≥ 4, it is shown that
$rc_{n-3}(Pₙ) ≤ \binom{n-2} {2}$
Upper and lower bounds are also presented for rcₖ(Pₙ) in terms of k when 1 ≤ k ≤ n- 1. The upper bound is shown to be sharp when 1 ≤ k ≤ 4 and n is sufficiently large.
Źródło:: Discussiones Mathematicae Graph Theory; 2004, 24, 1; 5-21
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 3.

Tytuł:: On Radio Connection Number of Graphs
Autorzy:: Marinescu-Ghemeci, Ruxandra
Powiązania:: https://bibliotekanauki.pl/articles/31343294.pdf
Data publikacji:: 2019-08-01
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: radio connection number
radio coloring
L (2, 1)-connection number
L (2, 1)-connectivity
L (2, 1)-labeling
Opis:: Given a graph G and a vertex coloring c, G is called l-radio connected if between any two distinct vertices u and v there is a path such that coloring c restricted to that path is an l-radio coloring. The smallest number of colors needed to make G l-radio connected is called the l-radio connection number of G. In this paper we introduce these notions and initiate the study of connectivity through radio colored paths, providing results on the 2-radio connection number, also called L(2, 1)-connection number: lower and upper bounds, existence problems, exact values for known classes of graphs and graph operations.
Źródło:: Discussiones Mathematicae Graph Theory; 2019, 39, 3; 705-730
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

Skocz do pozycji: 4.

Tytuł:: Distance coloring of the hexagonal lattice
Autorzy:: Jacko, Peter
Jendrol', Stanislav
Powiązania:: https://bibliotekanauki.pl/articles/744329.pdf
Data publikacji:: 2005
Wydawca:: Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
Tematy:: distance coloring
distant chromatic number
hexagonal lattice of the plane
hexagonal tiling
hexagonal grid
radio channel frequency assignment
Opis:: Motivated by the frequency assignment problem we study the d-distant coloring of the vertices of an infinite plane hexagonal lattice H. Let d be a positive integer. A d-distant coloring of the lattice H is a coloring of the vertices of H such that each pair of vertices distance at most d apart have different colors. The d-distant chromatic number of H, denoted $χ_d(H)$, is the minimum number of colors needed for a d-distant coloring of H. We give the exact value of $χ_d(H)$ for any d odd and estimations for any d even.
Źródło:: Discussiones Mathematicae Graph Theory; 2005, 25, 1-2; 151-166
2083-5892
Pojawia się w:: Discussiones Mathematicae Graph Theory
Dostawca treści:: Biblioteka Nauki

Artykuł

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