Matroids in terms of Cayley graphs and some related results
نویسندگان
چکیده
The point we try to get across is that the generalization of the counterparts of the matroid theory in Cayley graphs since the matroid theory frequently simplify the graphs and so Cayley graphs. We will show that, for a Cayley graph ΓG, the cutset matroid M ∗(ΓG) is the dual of the circuit matroid M(ΓG). We will also deduce that if Γ ∗ G is an abstract-dual of a Cayley graph Γ, then M(Γ∗ G ) is isomorphic to (M(ΓG)) ∗. 2000 Mathematics Subject Classification: 05C20; 05C25; 05C60.
منابع مشابه
On 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 کاملDomination parameters of Cayley graphs of some groups
In this paper, we investigate domination number, $gamma$, as well as signed domination number, $gamma_{_S}$, of all cubic Cayley graphs of cyclic and quaternion groups. In addition, we show that the domination and signed domination numbers of cubic graphs depend on each other.
متن کاملGraph product of generalized Cayley graphs over polygroups
In this paper, we introduce a suitable generalization of Cayley graphs that is defined over polygroups (GCP-graph) and give some examples and properties. Then, we mention a generalization of NEPS that contains some known graph operations and apply to GCP-graphs. Finally, we prove that the product of GCP-graphs is again a GCP-graph.
متن کاملDomination and Signed Domination Number of Cayley Graphs
In this paper, we investigate domination number as well as signed domination numbers of Cay(G : S) for all cyclic group G of order n, where n in {p^m; pq} and S = { a^i : i in B(1; n)}. We also introduce some families of connected regular graphs gamma such that gamma_S(Gamma) in {2,3,4,5 }.
متن کاملComputing Wiener and hyper–Wiener indices of unitary Cayley graphs
The unitary Cayley graph Xn has vertex set Zn = {0, 1,…, n-1} and vertices u and v are adjacent, if gcd(uv, n) = 1. In [A. Ilić, The energy of unitary Cayley graphs, Linear Algebra Appl. 431 (2009) 1881–1889], the energy of unitary Cayley graphs is computed. In this paper the Wiener and hyperWiener index of Xn is computed.
متن کامل