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Two classes of chromatically unique graphs

โœ Scribed by K.M. Koh; B.H. Goh


Publisher
Elsevier Science
Year
1990
Tongue
English
Weight
563 KB
Volume
82
Category
Article
ISSN
0012-365X

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โœฆ Synopsis


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.


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Classes of chromatically unique graphs
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The least number of colors needed to color the vertices of a graph G such that the vertices in each color class induces a linear forest is called the path-chromatic number of G, denoted by Zoo (G). If all such colorings of the vertices of G induce the same partitioning of the vertices of G, we say

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## Abstract In this paper, it is proven that for each __k__ โ‰ฅ 2, __m__ โ‰ฅ 2, the graph ฮ˜~__k__~(__m,โ€ฆ,m__), which consists of __k__ disjoint paths of length __m__ with same ends is chromatically unique, and that for each __m, n__, 2 โ‰ค __m__ โ‰ค __n__, the complete bipartite graph __K__~__m,n__~ is chr

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Du, Q., On o-polynomials and a class of chromatically unique graphs, Discrete Mathematics 115 (1993) 153-165. Let cr(G)=C:,,aicr '-' be the u-polynomial of a graph G. We ask the question: When k and a, are given, what is the largest possible value of ai(O < i < k) for any graph G? In this paper, thi