A new family of chromatically unique 6-bridge graph
نویسندگان
چکیده
منابع مشابه
Chromatically Unique Multibridge Graphs
Let θ(a1, a2, · · · , ak) denote the graph obtained by connecting two distinct vertices with k independent paths of lengths a1, a2, · · · , ak respectively. Assume that 2 ≤ a1 ≤ a2 ≤ · · · ≤ ak. We prove that the graph θ(a1, a2, · · · , ak) is chromatically unique if ak < a1 + a2, and find examples showing that θ(a1, a2, · · · , ak) may not be chromatically unique if ak = a1 + a2.
متن کاملClasses of chromatically unique graphs
Borowiecki, M. and E. Drgas-Burchardt, Classes of chromatically unique graphs, Discrete Mathematics Ill (1993) 71-75. We prove that graphs obtained from complete equibipartite graphs by deleting some independent sets of edges are chromatically unique. 1. Preliminary definitions and results In this paper we consider finite, undirected, simple and loopless graphs. Two graphs G and H are said to b...
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An h-uniform hypergraph (h ≥ 2) H = (V, E) of order n = |V| and size m = |E|, consists of a vertex set V(H) = V and edge set E(H) = E , where E ⊂ V and |E| = h for each edge E in E . H is said to be linear if 0 ≤ |E ∩ F | ≤ 1 for any two distinct edges E,F ∈ E(H) [1]. Let P h,1 p denote the linear path consisting of p ≥ 1 edges E1, . . . , Ep such that |E1| = . . . = |Ep| = h, |Ek ∩ El| = 1 if ...
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 کاملThe Chromatic Uniqueness of a Family of 6-Bridge Graphs
Let P (G,λ) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written G ∼ H, if P (G,λ) = P (H,λ). A graph G is chromatically unique, written χ−unique, if for any graph H, G ∼ H implies that G is isomorphic with H. In this paper we prove the chromatic uniqueness of a new family of 6-bridge graphs.
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ژورنال
عنوان ژورنال: Proyecciones (Antofagasta)
سال: 2018
ISSN: 0716-0917
DOI: 10.4067/s0716-09172018000200239