In her thesis [RB], Ranee Brylinski (then Gupta) studied the orbit structure of the projective variety of abelian subalgebras of a …xed dimension, k, in a simple Lie algebra, g, over C under its adjoint group, G. Fix a Borel subalgebra, b, of g and let B be the closed subgroup of G corresponding to b. Then the Borel …xed point theorem implies that the closed G-orbits are precisely the orbits of...

Suppose G is a simple connected n-vertex graph. Let σ3(G) denote the minimum degree sum of three independent vertices in G (which is ∞ ifG has no set of three independent vertices). A 2-trail is a trail that uses every vertex at most twice. Spanning 2-trails generalize hamilton paths and cycles. We prove three main results. First, if σ3(G) ≥ n−1, then G has a spanning 2-trail, unless G ∼= K1,3....

In this paper, we present two new generalizations of the pasting lemma using soft mixed structure. To do this, introduce notions a $(\tau _{1},\tau _{2})$-$g$-closed set and _{2})$-$gpr$% -closed set. We establish $g$-soft continuity $gpr$-soft between topological spaces $(X,\tau _{1},\Delta _{1})$, _{2},\Delta _{1})$ space ,\Delta _{2})$. Finally prove versions continuous mapping mapping.

The aim of the first part is to explain, how some geometric questions can be translated to the language of representation theory. There will be three categories of representations of G: Sm G ⊃ I G ⊃ Adm, roughly corresponding to birational geometry, to birational motivic questions (like structure of Chow groups of 0-cycles) and to " finite-dimensional " birational motivic questions (in particul...

In this paper we deal from an algorithmic perspective with different questions regarding properly edge-colored (or PEC) paths, trails and closed trails. Given a c-edge-colored graph G, we show how to polynomially determine, if any, a PEC closed trail subgraph whose number of visits at each vertex is specified before hand. As a consequence, we solve a number of interesting related problems. For ...

In this paper, a new class of generalized separation axioms (briefly, g-Tg-separation axioms) whose elements are called g-Tg,K, g-Tg,F, g-Tg,H, g-Tg,R, g-Tg,N-axioms is defined in terms sets g-Tg-sets) topological spaces Tg-spaces) and the properties characterizations Tg-space endowed with each such discussed. The study shows that g-Tg,F-axiom implies g-Tg,K-axiom, g-Tg,H-axiom g-Tg,F-axiom, g-...

A vertex v in a vertex-subset I of an undirected graph G is said to be redundant if its closed neighborhood is contained in the union of closed neighborhoods of vertices of I − {v}. In the context of a communication network , this means that any vertex that may receive communications from I may also be informed from I − {v} . The irredundance number ir(G) is the minimum cardinality taken over a...

Let G be a claw-free graph and let cl(G) be the closure of G. We present a method for characterizing classes G i , i = 3; : : : ; 7, of 2-connected closed claw-free graphs with the following properties.

For each vertex v in a graph G, let there be associated a subgraph Hv of G. The vertex v is said to dominate Hv as well as dominate each vertex and edge of Hv. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number γFH(G). A full dom...

For a graph G, a function f : V (G) ! f?1; 0; +1g is called a minus-domination function of G if the closed neighborhood of each vertex of G contains strictly more