The star clustering algorithm for static and dynamic information organization.
The star is the tree with greatest greatest Laplacian eigenvalue
The Steiner Minimal Network for Convex Configurations.
The Steiner Ratio Conjecture for Cocircular Points.
The Steiner Wiener Index of A Graph
The Wiener index W(G) of a connected graph G, introduced by Wiener in 1947, is defined as W(G) = ∑u,v∈V(G) d(u, v) where dG(u, v) is the distance between vertices u and v of G. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. For a connected graph G of order at least 2 and S ⊆ V (G), the Steiner distance d(S) of the vertices of S is the minimum size of a connected subgraph whose vertex set is S. We now...
The strong isometric dimension of finite reflexive graphs
The strong isometric dimension of a reflexive graph is related to its injective hull: both deal with embedding reflexive graphs in the strong product of paths. We give several upper and lower bounds for the strong isometric dimension of general graphs; the exact strong isometric dimension for cycles and hypercubes; and the isometric dimension for trees is found to within a factor of two.
The strong persistence property and symbolic strong persistence property
Let be an ideal in a commutative Noetherian ring . Then the ideal has the strong persistence property if and only if for all , and has the symbolic strong persistence property if and only if for all , where denotes the th symbolic power of . We study the strong persistence property for some classes of monomial ideals. In particular, we present a family of primary monomial ideals failing the strong persistence property. Finally, we show that every square-free monomial ideal has the...
The Strongly Asymmetric Graphs of Order 6 and 7
The strongly perfect lattices of dimension
This paper classifies the strongly perfect lattices in dimension . There are up to similarity two such lattices, and its dual lattice.
The strongly regular (40, 12, 2, 4) graphs.
The strongly regular (45, 12, 3, 3) graphs.
The structure and existence of 2-factors in iterated line graphs
We prove several results about the structure of 2-factors in iterated line graphs. Specifically, we give degree conditions on G that ensure L²(G) contains a 2-factor with every possible number of cycles, and we give a sufficient condition for the existence of a 2-factor in L²(G) with all cycle lengths specified. We also give a characterization of the graphs G where contains a 2-factor.
The structure of digraphs associated with the congruence
We assign to each pair of positive integers and a digraph whose set of vertices is and for which there is a directed edge from to if . We investigate the structure of . In particular, upper bounds are given for the longest cycle in . We find subdigraphs of , called fundamental constituents of , for which all trees attached to cycle vertices are isomorphic.
The structure of locally finite two-connected graphs.
The structure of maximal zero-sum free sequences
The structure of maximum subsets of with no solutions to .
The structure of plane graphs with independent crossings and its applications to coloring problems
If a graph G has a drawing in the plane in such a way that every two crossings are independent, then we call G a plane graph with independent crossings or IC-planar graph for short. In this paper, the structure of IC-planar graphs with minimum degree at least two or three is studied. By applying their structural results, we prove that the edge chromatic number of G is Δ if Δ ≥ 8, the list edge (resp. list total) chromatic number of G is Δ (resp. Δ + 1) if Δ ≥ 14 and the linear arboricity of G is...
The structure of standard modules, I: Universal algebras and the Rogers-Ramanujan identities.
The structure of superilat graphs
We prove a structure theorem asserting that each superflat graph is tree-decomposable in a very nice way. As a consequence we fully determine the spectrum functions of theories of superflat graphs.
The subalgebra lattice of a finite algebra
The aim of this paper is to characterize pairs (L, A), where L is a finite lattice and A a finite algebra, such that the subalgebra lattice of A is isomorphic to L. Next, necessary and sufficient conditions are found for pairs of finite algebras (of possibly distinct types) to have isomorphic subalgebra lattices. Both of these characterizations are particularly simple in the case of distributive subalgebra lattices. We do not restrict our attention to total algebras only, but we consider the more...