Chromatically Unique Multibridge Graphs

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...

Chromati ally Unique Multibridge Graphs

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 ...

Chromatic classes of 2-connected (n, n+4)-graphs with three triangles and one induced 4-cycle

For a graphG, let P(G, λ)be its chromatic polynomial. TwographsG andH are chromatically equivalent, denoted G ∼ H , if P(G, λ) = P(H, λ). A graph G is chromatically unique if P(H, λ) = P(G, λ) implies that H ∼= G. In this paper, we shall determine all chromatic equivalence classes of 2-connected (n, n+ 4)-graphs with three triangles and one induced 4-cycle, under the equivalence relation ‘ ∼’. ...

Chromaticity of certain tripartite graphs identified with a path

For a graphG, let P(G) be its chromatic polynomial. Two graphsG andH are chromatically equivalent if P(G)=P(H). A graph G is chromatically unique if P(H)= P(G) implies that H G. In this paper, we classify the chromatic classes of graphs obtained from K2,2,2 ∪ Pm(m 3), (K2,2,2 − e) ∪ Pm(m 5) and (K2,2,2 − 2e) ∪ Pm(m 6) by identifying the end-vertices of the path Pm with any two vertices of K2,2,...