Total and fractional total colourings of circulant graphs
نویسندگان
چکیده
منابع مشابه
Total and fractional total colourings of circulant graphs
In this paper, the total chromatic number and fractional total chromatic number of circulant graphs are studied. For cubic circulant graphs we give upper bounds on the fractional total chromatic number and for 4-regular circulant graphs we find the total chromatic number for some cases and we give the exact value of the fractional total chromatic number in most cases.
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Reed conjectured that for every > 0 and ∆ there exists g such that the fractional total chromatic number of a graph with maximum degree ∆ and girth at least g is at most ∆ + 1 + . We prove the conjecture for ∆ = 3 and for even ∆ ≥ 4 in the following stronger form: For each of these values of ∆, there exists g such that the fractional total chromatic number of any graph with maximum degree ∆ and...
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Cayley graph is a graph constructed out of a group Γ and a generating set A ⊆ Γ. When Γ = Zn, the corresponding Cayley graph is called as a circulant graph and denoted by Cir(n, A). In this paper, we attempt to find the total domination number of Cir(n, A) for a particular generating set A of Zn and a minimum total dominating set of Cir(n, A). Further, it is proved that Cir(n, A) is 2-total exc...
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A locating-total dominating set (LTDS) S of a graph G is a total dominating set S of G such that for every two vertices u and v in V(G) − S, N(u)∩S ≠ N(v)∩S. The locating-total domination number ( ) l t G is the minimum cardinality of a LTDS of G. A LTDS of cardinality ( ) l t G we call a ( ) l t G -set. In this paper, we determine the locating-total domination number for the special clas...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2008
ISSN: 0012-365X
DOI: 10.1016/j.disc.2007.11.070