The concepts of covering and matching in fuzzy graphs using strong arcs are introduced and obtained the relationship between them analogous to Gallai’s results in graphs. The notion of paired domination in fuzzy graphs using strong arcs is also studied. The strong paired domination number γspr of complete fuzzy graph and complete bipartite fuzzy graph is determined and obtained bounds for the s...

We shall prove that if L is a 3-chromatic (so called "forbidden") graph, and -R" is a random graph on n vertices, whose edges are chosen indepen-6" is a bipartite subgraph of R" of maximum size, -F" is an L-free subgraph of R" of maximum size, dently, with probability p, and then (in some sense) F" and 6" are very near to each other: almost surely they have almost the same number of edges, and ...

Orthogonal ray graphs are the intersection graphs of horizontal and vertical rays (i.e. half-lines) in the plane. If the rays can have any possible orientation (left/right/up/down) then the graph is a 4-directional orthogonal ray graph (4-DORG). Otherwise, if all rays are only pointing into the positive x and y directions, the intersection graph is a 2-DORG. Similarly, for 3-DORGs, the horizont...

Let q be a prime power, Fq be the field of q elements, and k;m be positive integers. A bipartite graph G 1⁄4 Gqðk;mÞ is defined as follows. The vertex set of G is a union of two copies P and L of two-dimensional vector spaces over Fq, with two vertices ðp1;p2Þ 2 P and 1⁄2 l1; l2 2 L being adjacent if and only if p2 þ l2 1⁄4 p 1 l 1 . We prove that graphs Gqðk ;mÞ and Gq0 ðk 0;m0Þ are isomorphic...

In this paper we shall consider ordinary graphs, that is, graphs without loops and multiple edges . Given a graph L, ex(n , L) will denote the maximum number of edges a graph G" of order n can have without containing any L . Determining ex(n,L), or at least finding good bounds on it will be called TURÁN TYPE EXTREMAL PROBLEM. Assume that a graph G" has E > ex(n , L) edges. Then it must contain ...

number of k-subsets of an n-set so that the size of the intersection of any two among them is in L. It is proven that for every rational number r 2 1 there is a choice of k and L so that cn'<m(n, k, L) idn', where c, d depend on k and L but not on n. 0 1986 Academic Press. Inc

A graph has hyuiciry k if k is the smallest integer such that G is an intersection graph of k-dimensional boxes in a &-dimensional space (where the sides of the boxes are parallel to the coordinate axis). A graph has grid dimension k if k is the smallest integer such that G is an intersection graph of k-dimensional boxes (parallel to the coordinate axis) in a (k+ I)-dimensional space. We prove ...

We investigate the intersection of two finitely generated submonoids of the free monoid on a finite alphabet A. To this purpose, we consider automata that recognize such submonoids and we study the product automata recognizing their intersection. By using automata methods we obtain a new proof of a result of Karhumäki on the characterization of the intersection of two submonoids of rank two, in...

The amalgamation of cluster varieties introduced by Fock and Goncharov in [21] plays a relevant role both mathematical physical problems. In particular, the totally non-negative part positroid is explicitly described as gluing several copies small positive Grassmannians, GrTP(1,3) GrTP(2,3), has important topological implications [53] naturally appears computation amplitude scatterings N=4 SYM ...