On chromaticity of graphs
نویسنده
چکیده
Abstract In this paper we obtain the explicit formulas for chromatic polynomials of cacti. From the results relating to cacti we deduce the analogous formulas for the chromatic polynomials of n–gon–trees. Besides, we characterize unicyclic graphs by their chromatic polynomials. We also show that the so–called clique–forest–like graphs are chromatically equivalent.
منابع مشابه
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...
متن کاملA 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...
متن کاملChromaticity 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...
متن کاملChromaticity 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...
متن کاملOn 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 ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discussiones Mathematicae Graph Theory
دوره 15 شماره
صفحات -
تاریخ انتشار 1995