The aim of this paper is to introduce and study two new classes of functions called weakly $e^{*}$-open functions and weakly $e^{*}$-closed functions via the concept of $e^{*}$-open set defined by Ekici cite{erd1}. The notions of weakly $e^{*}$-open and weakly $e^{*}$-closed functions are weaker than the notions of weakly $beta$-open and weakly $beta$-closed functions defined by Caldas and Nava...

In this paper we determine completely the class of binary matroids with no minors isomor-phic to the cycle matroid of the prism graph M*(Ks\e), its dual M(Ks\e), and the binary affine cube AG(3, 2).

Let G = (V,E) be a graph of order n. A closed distance magic labeling of G is a bijection l : V (G) → {1, . . . , n} for which there exists a positive integer k such that ∑ x∈N [v] l(x) = k for all v ∈ V , where N [v] is the closed neighborhood of v. We consider the closed distance magic graphs in the algebraic context. In particular we analyze the relations between the closed distance magic la...

Let $G$ be a graph with $p$ vertices and $q$ edges. The graph $G$ is said to be a super pair sum labeling if there exists a bijection $f$ from $V(G)cup E(G)$ to ${0, pm 1, pm2, dots, pm (frac{p+q-1}{2})}$ when $p+q$ is odd and from $V(G)cup E(G)$ to ${pm 1, pm 2, dots, pm (frac{p+q}{2})}$ when $p+q$ is even such that $f(uv)=f(u)+f(v).$ A graph that admits a super pair sum labeling is called a {...

let f, g and h be non-empty graphs. the notation f → (g,h) means that if any edge of f is colored by red or blue, then either the red subgraph of f con- tains a graph g or the blue subgraph of f contains a graph h. a graph f (without isolated vertices) is called a ramsey (g,h)−minimal if f → (g,h) and for every e ∈ e(f), (f − e) 9 (g,h). the set of all ramsey (g,h)−minimal graphs is denoted by ...

We show that for a continuous map of a closed interval to itself, if the set of periodic points is closed, then every recurrent point is periodic. If, furthermore, the set of least periods of the periodic points is finite, then every nonwandering point is periodic. This answers a question of L. Block [Proc. Amer. Math. Soc. 67 (1977), 357-360]. Introduction. In [1] and [2], L. Block studied con...

Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as:     ( ) ( , ) [ ] e uv E G G x x d(u) + d(v) M1 , ( , )  euvE(G) G x x|d(u) - d(v)| M3 . In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.

A graph G = (V, E) is said to be represented by a family F of nonempty sets if there is a bijection f:V--*F such that uv ~ E if and only iff(u)Nf(v)q=~. It is proved that if G is a countable graph then G can be represented by open intervals on the real line if and only if G can be represented by closed intervals on the real line, however, this is no longer true when G is an uncountable graph. S...

let g be a (p, q) graph. let k be an integer with 2 ≤ k ≤ p and f from v (g) to the set {1, 2, . . . , k} be a map. for each edge uv, assign the label |f(u) − f(v)|. the function f is called a k-difference cordial labeling of g if |νf (i) − vf (j)| ≤ 1 and |ef (0) − ef (1)| ≤ 1 where vf (x) denotes the number of vertices labelled with x (x ∈ {1, 2 . . . , k}), ef (1) and ef (0) respectively den...

Let F, G and H be non-empty graphs. The notation F → (G,H) means that if any edge of F is colored by red or blue, then either the red subgraph of F con- tains a graph G or the blue subgraph of F contains a graph H. A graph F (without isolated vertices) is called a Ramsey (G,H)−minimal if F → (G,H) and for every e ∈ E(F), (F − e) 9 (G,H). The set of all Ramsey (G,H)−minimal graphs is denoted by ...