TWO USES FOR GRAPHS

A CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION

‎The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$‎. ‎In this case‎, ‎$B$ is called a textit{metric basis} for $G$‎. ‎The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$‎. ‎Givi...

On two-dimensional Cayley graphs

A subset W of the vertices of a graph G is a resolving set for G when for each pair of distinct vertices u,v in V (G) there exists w in W such that d(u,w)≠d(v,w). The cardinality of a minimum resolving set for G is the metric dimension of G. This concept has applications in many diverse areas including network discovery, robot navigation, image processing, combinatorial search and optimization....

Uses Of C-Graphs In A Prototype For Altomatic Twislation

This paper presents a prototype, not completely operational, that is intended to use c-graphs in the translation of assemblers. Firstly, the formalization of the structure and its principal notions (substructures, classes of substructures, order, etc.) are presented. Next section describes the prototype which is based on a Transformational System as well as on a rewriting system of c-graphs whi...

Extremal Subgraphs for Two Graphs

In this paper we study several interrelated extremal graph problems : (i) Given integers n, e, m, what is the largest integer f(n, e, m) such that every graph with n vertices and e edges must have an induced m-vertex subgraph with at least f(n, e, m) edges? (ü) Given integers n, e, e', what is the largest integer g(n, e, e') such that any two n-vertex graphs G and H, with e and e' edges, respec...

Part Two USES OF MORTALITY DATA