Let G = (V,E) be a connected undirected graph. For any vertex v ∈ V , the closed neighborhood of v is N [v] = {v} ∪ {u ∈ V | uv ∈ E }. For S ⊆ V , the closed neighborhood of S is N [S] = ⋃ v∈S N [v]. The subgraph weakly induced by S is 〈S〉w = (N [S], E ∩ (S × N [S])). A set S is a weakly-connected dominating set of G if S is dominating and 〈S〉w is connected. The weakly-connected domination numb...

we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .

for a finite group $g$‎, ‎we study the total character $tau_g$‎ ‎afforded by the direct sum of all the non-isomorphic irreducible‎ ‎complex representations of $g$‎. ‎we resolve for several classes of‎ ‎groups (the camina $p$-groups‎, ‎the generalized camina $p$-groups‎, ‎the groups which admit $(g,z(g))$ as a generalized camina pair)‎, ‎the problem of existence of a‎ ‎polynomial $f(x) in mathbb...

An interesting observation is that most pairs of weakly homogeneous mappings do not possess strongly monotonic property, which one the key conditions to ensure unique solvability generalized variational inequality. This paper focuses on studying uniqueness and inequality with a pair mappings. By using weaker condition than strong monotonicity some additional conditions, we achieve several resul...

We define the notions of weakly μ-countably compactness and nearly denoted by Wμ-CC Nμ-CC as generalizations μ-compact spaces in sense Csaśzaŕ generalized topological spaces. To obtain a more general setting, we via hereditary classes. Using μθ-open sets, μ-regular open spaces, many results characterizations have been presented. Moreover, use properties functions to investigate effects some typ...