Independence equivalence classes of cycles

Chromatic equivalence classes of certain cycles with edges

Let P(G) denote the chromatic polynomial of a graph G. Two graphs G and H are chromatically equivalent, written G∼H , if P(G) = P(H). A graph G is chromatically unique if for any graph H , G∼H implies that G is isomorphic with H . In this paper, we give the necessary and su:cient conditions for a family of generalized polygon trees to be chromatically unique. c © 2001 Elsevier Science B.V. All ...

The graph of equivalence classes and Isoclinism of groups

‎Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$‎. ‎In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$‎, ‎where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$‎. ‎We introduce a new graph determined ...

Some equivalence classes of operators on B(H)

On the Domination of Cartesian Product of Directed Cycles: Results for Certain Equivalence Classes of Lengths

Let γ( −→ Cm2 −→ Cn) be the domination number of the Cartesian product of directed cycles −→ Cm and −→ Cn for m,n ≥ 2. Shaheen [13] and Liu et al. ([11], [12]) determined the value of γ( −→ Cm2 −→ Cn) when m ≤ 6 and [12] when both m and n ≡ 0(mod 3). In this article we give, in general, the value of γ(−→ Cm2 −→ Cn) when m ≡ 2(mod 3) and improve the known lower bounds for most of the remaining c...

Fuzzy equivalence relations and their equivalence classes

In this paper we investigate various properties of equivalence classes of fuzzy equivalence relations over a complete residuated lattice. We give certain characterizations of fuzzy semipartitions and fuzzy partitions over a complete residuated lattice, as well as over a linearly ordered complete Heyting algebra. In the latter case, for a fuzzy equivalence relation over a linearly ordered comple...