On chromaticity of graphs

Chromaticity of Turan Graphs with At Most Three Edges Deleted

Let $P(G,lambda)$ be the chromatic polynomial of a graph $G$. A graph $G$ ischromatically unique if for any graph $H$, $P(H, lambda) = P(G,lambda)$ implies $H$ is isomorphic to $G$. In this paper, we determine the chromaticity of all Tur'{a}n graphs with at most three edges deleted. As a by product, we found many families of chromatically unique graphs and chromatic equivalence classes of graph...

A new result on chromaticity of K4-homoemorphs with girth 9

For a graph $G$, let $P(G,lambda)$ denote the chromatic polynomial of $G$. Two graphs $G$ and $H$ are chromatically equivalent if they share the same chromatic polynomial. A graph $G$ is chromatically unique if any graph chromatically equivalent to $G$ is isomorphic to $G$. A $K_4$-homeomorph is a subdivision of the complete graph $K_4$. In this paper, we determine a family of chromatically uni...

Chromaticity of Complete 6-Partite Graphs with Certain Star or Matching Deleted

Let P (G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ∼ H, if P (G,λ) = P (H,λ). We write [G] = {H|H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 6-partite graphs with 6n vertices according to the number of 7-independent partitions of G. Using these resul...

Chromaticity of Complete Tripartite Graphs With Certain Star or Matching Deleted

Let P (G, λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G ∼ H, if P (G, λ) = P (H, λ). We write [G] = {H|H ∼ G}. If [G] = {G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 6-partite graphs with 6n vertices according to the number of 7-independent partitions of G. Using these re...

On Chromaticity of Wheels

Let the vertices of a graph such that every two adjacent vertices have different color is a very common problem in the graph theory. This is known as proper coloring of graphs. The possible number of different proper colorings on a graph with a given number of colors can be represented by a function called the chromatic polynomial. Two graphs G and H are said to be chromatically equivalent, if ...

Chromaticity of the Complements of Some Sparse Graphs