we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

in this paper, we define the common minimal common neighborhooddominating signed graph (or common minimal $cn$-dominating signedgraph) of a given signed graph and offer a structuralcharacterization of common minimal $cn$-dominating signed graphs.in the sequel, we also obtained switching equivalencecharacterization: $overline{sigma} sim cmcn(sigma)$, where$overline{sigma}$ and $cmcn(sigma)$ are ...

In Collaborative Network (CN) environments, creation of collective understanding about both the aimed outcome and the procedure for achieving it by its members is the antecedent to any successful co-working and codevelopment. While a part of the common CN knowledge is pre-existing to its establishment, once the collaboration activities begin the emergent knowledge also needs to be commonly unde...

We prove that a germ of a holomorphic map f between Cn and Cn ′ sending one real-algebraic submanifold M ⊂ Cn into another M ′ ⊂ Cn ′ is algebraic provided M ′ contains no complex-analytic discs and M is generic and minimal. We also propose an algorithm for finding complex-analytic discs in a real submanifold.

Let Cn be the cyclic group of n elements, and let S = (a1, · · · , ak) be a sequence of elements in Cn. We say that S is a zero sequence if ∑k i=1 ai = 0 and that S is a minimal zero-sequence if S is a zero sequence and S contains no proper zero subsequence. In this paper we prove, among other results, that if S is a minimal zero sequence of elements in Cn and |S| ≥ n − [ 3 ] + 1, then there ex...

The topic of the paper is the study of germs of local holomorphisms f between Cn and Cn ′ such that f(M) ⊂ M ′ and df(T cM) = T cM ′ for M ⊂ Cn and M ′ ⊂ Cn generic real-analytic CR submanifolds of arbitrary codimensions. It is proved that for M minimal and M ′ finitely nondegenerate, such germs depend analytically on their jets. As a corollary, an analytic structure on the set of all germs of ...