Displaying similar documents to “Color Energy Of A Unitary Cayley Graph”

Solutions of Some L(2, 1)-Coloring Related Open Problems

Nibedita Mandal, Pratima Panigrahi (2016)

Discussiones Mathematicae Graph Theory

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An L(2, 1)-coloring (or labeling) of a graph G is a vertex coloring f : V (G) → Z+ ∪ {0} such that |f(u) − f(v)| ≥ 2 for all edges uv of G, and |f(u)−f(v)| ≥ 1 if d(u, v) = 2, where d(u, v) is the distance between vertices u and v in G. The span of an L(2, 1)-coloring is the maximum color (or label) assigned by it. The span of a graph G is the smallest integer λ such that there exists an L(2, 1)-coloring of G with span λ. An L(2, 1)-coloring of a graph with span equal to the span of...

Vertex coloring the square of outerplanar graphs of low degree

Geir Agnarsson, Magnús M. Halldórsson (2010)

Discussiones Mathematicae Graph Theory

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Vertex colorings of the square of an outerplanar graph have received a lot of attention recently. In this article we prove that the chromatic number of the square of an outerplanar graph of maximum degree Δ = 6 is 7. The optimal upper bound for the chromatic number of the square of an outerplanar graph of maximum degree Δ ≠ 6 is known. Hence, this mentioned chromatic number of 7 is the last and only unknown upper bound of the chromatic number in terms of Δ.

On the Total Graph of Mycielski Graphs, Central Graphs and Their Covering Numbers

H.P. Patil, R. Pandiya Raj (2013)

Discussiones Mathematicae Graph Theory

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The technique of counting cliques in networks is a natural problem. In this paper, we develop certain results on counting of triangles for the total graph of the Mycielski graph or central graph of star as well as completegraph families. Moreover, we discuss the upper bounds for the number of triangles in the Mycielski and other well known transformations of graphs. Finally, it is shown that the achromatic number and edge-covering number of the transformations mentioned above are equated. ...

2-Tone Colorings in Graph Products

Jennifer Loe, Danielle Middelbrooks, Ashley Morris, Kirsti Wash (2015)

Discussiones Mathematicae Graph Theory

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A variation of graph coloring known as a t-tone k-coloring assigns a set of t colors to each vertex of a graph from the set {1, . . . , k}, where the sets of colors assigned to any two vertices distance d apart share fewer than d colors in common. The minimum integer k such that a graph G has a t- tone k-coloring is known as the t-tone chromatic number. We study the 2-tone chromatic number in three different graph products. In particular, given graphs G and H, we bound the 2-tone chromatic...

Equitable coloring of Kneser graphs

Robert Fidytek, Hanna Furmańczyk, Paweł Żyliński (2009)

Discussiones Mathematicae Graph Theory

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The Kneser graph K(n,k) is the graph whose vertices correspond to k-element subsets of set {1,2,...,n} and two vertices are adjacent if and only if they represent disjoint subsets. In this paper we study the problem of equitable coloring of Kneser graphs, namely, we establish the equitable chromatic number for graphs K(n,2) and K(n,3). In addition, for sufficiently large n, a tight upper bound on equitable chromatic number of graph K(n,k) is given. Finally, the cases of K(2k,k) and K(2k+1,k)...