Interval function of a graph is well-known notion in metric theory and the axiomatic characterization using set first order axioms different classes an interesting problem this area. Partial cubes partial Hamming graphs form one central class that can be embedded into hypercubes respectively. In paper we present interval graphs, axioms. Further, give these on arbitrary R V.

let $g$ be a finite group. we construct the prime graph of $ g $,which is denoted by $ gamma(g) $ as follows: the vertex set of thisgraph is the prime divisors of $ |g| $ and two distinct vertices $ p$ and $ q $ are joined by an edge if and only if $ g $ contains anelement of order $ pq $.in this paper, we determine finite groups $ g $ with $ gamma(g) =gamma(l_3(q)) $, $2 leq q < 100 $ and prov...

We present a linear time algorithm for the minimum linear arrangement problem on proper interval graphs. The obtained ordering is a 4-approximation for general interval graphs. 1 Preliminaries Let F be a family of nonempty sets. The intersection graph of F is obtained by representing each set in F by a vertex and connecting two vertices by an edge if and only if their corresponding sets interse...

A Set S of vertices in a graph G(V,E) is called dominating set,if every vertex v V id either an element or adjacent to S. vertice Total set if S, total G with no isolated subset the such that In this paper we will find perfect Interval graph. We also out induced subgraph regarding which were splitted.