The chromatic number of 5-valent circulants
نویسندگان
چکیده
A circulant C(n; S) with connection set S = {a1, a2, . . . , am} is the graph with vertex set Zn , the cyclic group of order n, and edge set E = {{i, j} : |i − j | ∈ S}. The chromatic number of connected circulants of degree at most four has been previously determined completely by Heuberger [C. Heuberger, On planarity and colorability of circulant graphs, Discrete Math. 268 (2003) 153–169]. In this paper, we determine completely the chromatic number of connected circulants C(n; a, b, n/2) of degree 5. The methods used are essentially extensions of Heuberger’s method but the formulae developed are much more
منابع مشابه
Circulants and the Chromatic Index of Steiner Triple Systems
We complete the determination of the chromatic number of 6valent circulants of the form C(n; a, b, a+b) and show how this can be applied to improving the upper bound on the chromatic index of cyclic Steiner triple systems.
متن کاملOn 4-valent Frobenius circulant graphs
A 4-valent first-kind Frobenius circulant graph is a connected Cayley graph DLn(1, h) = Cay(Zn, H) on the additive group of integers modulo n, where each prime factor of n is congruent to 1 modulo 4 and H = {[1], [h],−[1], −[h]} with h a solution to the congruence equation x + 1 ≡ 0 (mod n). In [A. Thomson and S. Zhou, Frobenius circulant graphs of valency four, J. Austral. Math. Soc. 85 (2008)...
متن کاملOn Circulants Uniquely Characterized by their Independence Polynomials
In [18], Farrell and Whitehead investigate circulant graphs that are uniquely characterized by their matching and chromatic polynomials (i.e., graphs that are “matching unique” and “chromatic unique”). They develop a partial classification theorem, by finding all matching unique and chromatic unique circulants on n vertices, for each n ≤ 8. In this paper, we explore circulant graphs that are un...
متن کاملCirculants and Sequences
A graph G is stable if its normalized chromatic difference sequence is equal to the normalized chromatic di erence sequence of G G, the Cartesian product of G with itself. Let be the independence number of G and ! be its clique number. Suppose that G has n vertices. We show that the rst ! terms of the normalized chromatic di erence sequence of a stable graph G must be =n; and further that if G ...
متن کاملFrobenius circulant graphs of valency six, Eisenstein-Jacobi networks, and hexagonal meshes
A finite Frobenius group is a permutation group which is transitive but not regular such that only the identity element can fix two points. Such a group can be expressed as a semidirect product G = K o H, where K is a nilpotent normal subgroup. A first-kind G-Frobenius graph is a Cayley graph on K whose connection set is an H-orbit S on K that generates K, where H is of even order or S consists...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Discrete Mathematics
دوره 308 شماره
صفحات -
تاریخ انتشار 2008