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A generalization of chromatic polynomial of a graph subdivision

✍ Scribed by D. M. Cardoso; M. E. Silva; J. Szymański

Book ID
113072800
Publisher
Springer US
Year
2012
Tongue
English
Weight
167 KB
Volume
182
Category
Article
ISSN
1573-8795

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📜 SIMILAR VOLUMES

A Symmetric Function Generalization of t
A Symmetric Function Generalization of the Chromatic Polynomial of a Graph
✍ R.P. Stanley 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 932 KB

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 \(n\).

On chromatic uniqueness of uniform subdi
On chromatic uniqueness of uniform subdivisions of graphs
✍ C.P. Teo; K.M. Koh 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 492 KB

Let u,(G) denote the number of cycles of length k in a graph G. In this paper, we first prove that if G and H are X-equivalent graphs, then ak(G) = a,(H) for all k with g < k < $g -2, where g is the girth of G. This result will then be incorporated with a structural theorem obtained in [7] to show t