Chromatic uniqueness of the generalized θ-graph
✍ Scribed by Beatrice Loerinc
- Publisher
- Elsevier Science
- Year
- 1978
- Tongue
- English
- Weight
- 323 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
A generalized O-graph i.~ a wnnected graph with 3 palths between a pair of vertices of degree 3. It is showi:~ that uny graph having the same ckomatic polynomial as a generaiized O-graph, must be isomorphic to tk generalized O-graph.
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Xu, S., The chromatic uniqueness of complete bipartite graphs, Discrete Mathematics 94 (1991) 153-159. This paper is partitioned into two parts. In the first part we determine the maximum number of induced complete bipartite subgraphs in graphs with some given conditions. Using a theorem given in th
## Let P(G; A) denote the chromatic polynomial of a graph G. G is chromatically unique if G is isomorphic to H for any graph H with P(H; A) = P(G; A). In this paper, we provide two new classes of chromatically unique graphs.
## Abstract A graph is chromatically unique if it is uniquely determined by its chromatic polynomial. Let __G__ be a chromatically unique graph and let __K__~__m__~ denote the complete graph on __m__ vertices. This paper is mainly concerned with the chromaticity of __K__~__m__~ + __G__ where + deno