## Abstract In this paper we obtain chromatic polynomials of connected 3β and 4βchromatic planar graphs that are maximal for positive integerβvalued arguments. We also characterize the class of connected 3βchromatic graphs having the maximum number of __p__βcolorings for __p__ β₯ 3, thus extending a
The chromatic polynomial of an unlabeled graph
β Scribed by P Hanlon
- Publisher
- Elsevier Science
- Year
- 1985
- Tongue
- English
- Weight
- 615 KB
- Volume
- 38
- Category
- Article
- ISSN
- 0095-8956
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π SIMILAR VOLUMES
## Abstract In this paper we obtain chromatic polynomials __P(G__; Ξ») of 2βconnected graphs of order __n__ that are maximum for positive integerβvalued arguments Ξ» β§ 3. The extremal graphs are cycles __C__~__n__~ and these graphs are unique for every Ξ» β§ 3 and __n__ β 5. We also determine max{__P(
For a finite graph \(G\) with \(d\) vertices we define a homogeneous symmetric function \(X_{4 ;}\) of degree \(d\) in the variables \(x_{1}, x_{2}, \ldots\). If we set \(x_{1}=\cdots=x_{n}=1\) and all other \(x_{t}=0\), then we obtain \(Z_{1}(n)\), the chromatic polynomial of (; evaluated at \(n\).
## Abstract In the set of graphs of order __n__ and chromatic number __k__ the following partial order relation is defined. One says that a graph __G__ is less than a graph __H__ if __c__~__i__~(__G__) β€ __c__~__i__~(__H__) holds for every __i__, __k__ β€ __i__ β€ __n__ and at least one inequality is
Frucht and Giudici classified all graphs having quadratic a-polynomials. Here w e classify all chromatically unique graphs having quadratic (Tpolynomials.
The chromatic polynomial ;X chromial) of a graph was first defined by Birkhoff in 1912, ;md gives the number of ways or" properly colov iing the vertices of the graph with any number of colours. A good survey of the b-sic facts about these polynomials may be found in the article by Read [ 3 3 . It