We discuss some implications of linear programming for Mather theory [Mt1-2], [M-F] and its finite dimensional approximations. We find that the complementary slackness condition of duality theory formally implies that the Mather set lies in an n–dimensional graph and as well predicts the relevant nonlinear PDE for the “weak KAM” theory of Fathi [F1-3], [E-G]. In memory of Professor Jacques–Loui...

A model-based approach for minimization of test sets for interactive systems is introduced. Test cases are efficiently generated and selected to cover the behavioral model and the complementary fault model of the system under test (SUT). Results known from state-based conformance testing and graph theory are used and extended to construct algorithms for minimizing the test sets, considering als...

The interactional structure of learning practices is a central focus of study for CSCL. Different approaches produce complementary insights, but rely on incompatible notations for their results, creating challenges in comparing and contrasting different analyses. Building on recent analytic work within our laboratory, we propose an analysis methodology consisting of a unifying theoretical found...

This article reports on a research project investigating the following two complementary issues: (1) improving how the structure of XML and HTML can be specified, (2) using structure specification (of XML and HTML documents) for static type checking of Web (and Semantic Web) query programs. The first step towards this goal is to provide a schema language like DTD, XML Schema or Relax-NG with be...

Jwo et al. [Networks 23 (1993) 315–326] introduced the alternating group graph as an interconnection network topology for computing systems. They showed that the proposed structure has many advantages over n-cubes and star graphs. For example, all alternating group graphs are hamiltonian-connected (i.e., every pair of vertices in the graph are connected by a hamiltonian path) and pancyclic (i.e...

altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. we now provide a generalization of the altan concept, applicable to any graph. several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. among these ar...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex v and f*(v (g)) is either of the form {±k1,±k2,...,±kp/2} or {±k1,±k2,...,±k(p-1)/2} u {±k(p+1)/2} according a...

The first and second zagreb indices of a graph G are defined as M1(G) = ∑ uv∈E(G) [deg(u) + deg(v)] (or equivalently ∑ u∈V (G) [deg(u)2] and M2(G) = ∑ uv∈E(G) [deg(u)deg(v)] respectively. In this paper, we have obtained the first and second zagreb indices of the generalized complementary prisms Gm+n,Gm,n,G m,m and Gm,m. MSC: 05C15, 05C38.

A method to control the application of equality derivation rules in an automatic theorem proving system is presented. When handling equality in the search for a proof of a theorem two main problems arise: 1) to obtain a control mechanism for the search and application of useful equality derivation steps in order to support global strategies which plan and control the whole proof, thus conducing...

Spectral graph theory is undoubtedly the most favored graph data analysis technique, both in theory and practice. It has emerged as a versatile tool for a wide variety of applications including data mining, web search, quantum computing, computer vision, image segmentation, and among others. However, the way in which spectral graph theory is currently taught and practiced is rather mechanical, ...