Let G = (V,E) be a connected graph (or hypergraph) and let d(x, y) denote the distance between vertices x, y ∈ V (G). A subset W ⊆ V (G) is called a resolving set for G if for every pair of distinct vertices x, y ∈ V (G), there is w ∈ W such that d(x,w) 6= d(y, w). The minimum cardinality of a resolving set for G is called the metric dimension of G, denoted by β(G). The circulant graph Cn(1, 2,...

A minimal cutset of a tree directed from the leaves to the root is a minimal set of vertices such that every path from a leaf to the root meets at least one of these vertices. An order relation on the set of minmal cutsets can be deened: U V if and only if every vertex of U is on the path from some vertex in V to the root. Motivated by the design of eecient cryptographic digital signature schem...

For an affine Lie algebra ĝ, the coefficients of certain vertex operators that annihilate level k standard ĝ-modules are defining relations for modules. In this paper, we study a combinatorial structure leading terms these = 2 algebras type Cn(1) and main result is construction combinatorially parameterized among annihilating fields. It believed constructed will play key role in Gröbner-like ba...