we show that the character space of the vector-valued lipschitz algebra $lip^{alpha}(x, e)$ of order $alpha$ is homeomorphic to the cartesian product $xtimes m_e$ in the product topology, where $x$ is a compact metric space and $e$ is a unital commutative banach algebra. we also characterize the form of each character on $lip^{alpha}(x, e)$. by appealing to the injective tensor product, we then...

An outer-connected dominating set for an arbitrary graph G is a set D̃ ⊆ V such that D̃ is a dominating set and the induced subgraph G[V \ D̃] be connected. In this paper, we focus on the outerconnected domination number of the product of graphs. We investigate the existence of outer-connected dominating set in lexicographic product and Corona of two arbitrary graphs, and we present upper bounds f...

In this paper, we give a characterization of strongly Jordan zero-product preserving maps on normed algebras as a generalization of  Jordan zero-product preserving maps. In this direction, we give some illustrative examples to show that the notions of strongly zero-product preserving maps and strongly Jordan zero-product preserving maps are completely different. Also, we prove that the direct p...

Let D = (V,E) be a digraph and u, v ∈ V. The metric maximum distance is defined by md(u,v) max {d⃗(u,v), d⃗(v,u)}, where d⃗(u,v) denote the length of shortest directed u − path in D. m-eccentricity vertex mecc(v) {md(v,u) : V(D)}. m-center mC(D) strongly connected consists all vertices with minimum m-eccentricity, m-periphery mPer(D) relationship between two digraphs their lexicographic product st...