CLIQUE NUMBERS OF GRAPHS AND IRREDUCIBLE EXACT m-COVERS OF Z
نویسنده
چکیده
For each m ≥ 1, we construct a graph G = (V, E) with ω(G) = m such that max 1≤i≤k ω(G[Vi]) = m for arbitrary partition V = V1 ∪ · · · ∪ Vk, where ω(G) is the clique number of G and G[Vi] is the induced graph of Vi. Using this result, we show that for each m ≥ 2 there exists an exact m-cover of Z which is not the union of two 1-covers.
منابع مشابه
Irreducible Exact Covering Systems and Clique Numbers of Graphs
For each m ≥ 1, we construct a graph G = (V, E) with ω(G) = m such that max i=1,2 ω(ind(Vi)) = m for arbitrary partition V = V1 ∪ V2, where ω(G) is the clique number of G and ind(Vi) is the induced graph of Vi. Using this result, we may show that for each m ≥ 2 there exists an exact m-cover of Z which is not the union of two 1-covers.
متن کاملClique irreducibility of some iterative classes of graphs
In this paper, two notions, the clique irreducibility and clique vertex irreducibility are discussed. A graph G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and it is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G. It is proved that L(G) is clique irreducible if a...
متن کاملClique Irreducibility and Clique Vertex Irreducibility of Graphs
A graphs G is clique irreducible if every clique in G of size at least two, has an edge which does not lie in any other clique of G and is clique reducible if it is not clique irreducible. A graph G is clique vertex irreducible if every clique in G has a vertex which does not lie in any other clique of G and clique vertex reducible if it is not clique vertex irreducible. The clique vertex irred...
متن کاملVertex-transitive CIS graphs
A CIS graph is a graph in which every maximal stable set and every maximal clique intersect. A graph is well-covered if all its maximal stable sets are of the same size, co-well-covered if its complement is well-covered, and vertex-transitive if, for every pair of vertices, there exists an automorphism of the graph mapping one to the other. We show that a vertex-transitive graph is CIS if and o...
متن کاملOn the distance eigenvalues of Cayley graphs
In this paper, we determine the distance matrix and its characteristic polynomial of a Cayley graph over a group G in terms of irreducible representations of G. We give exact formulas for n-prisms, hexagonal torus network and cubic Cayley graphs over abelian groups. We construct an innite family of distance integral Cayley graphs. Also we prove that a nite abelian group G admits a connected...
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:
دوره شماره
صفحات -
تاریخ انتشار 2008