a graph is called textit{circulant} if it is a cayley graph on a cyclic group, i.e. its adjacency matrix is circulant. let $d$ be a set of positive, proper divisors of the integer $n>1$. the integral circulant graph $icg_{n}(d)$ has the vertex set $mathbb{z}_{n}$ and the edge set e$(icg_{n}(d))= {{a,b}; gcd(a-b,n)in d }$. let $n=p_{1}p_{2}cdots p_{k}m$, where $p_{1},p_{2},cdots,p_{k}$ are disti...

in this paper, we introduce and characterize fuzzy wea-kly $e$-closed functions in fuzzy topological spaces and the relationship between these mappings and some properties of them are investigated.

The strong embedding conjecture states that every 2-connected graph has a closed 2-cell embedding in some surface , i . e . an embedding that each face is bounded by a circuit in the graph . A graph is called k -crosscap embeddable if it can be embedded in the surface of non-orientable genus k . We confirm the strong embedding conjecture for 5-crosscap embeddable graphs . As a corollary , every...

We completely describe the structure of irreducible integral flows on a signed graph by lifting them to the signed double covering graph. A (real-valued) flow (sometimes also called a circulation) on a graph or a signed graph (a graph with signed edges) is a real-valued function on oriented edges, f : ~ E → R, such that the net inflow to any vertex is zero. An integral flow is a flow whose valu...

A graph G=(V; E) is a tolerance graph if there is a set I={Iv | v∈V} of closed real intervals and a set ={ v | v∈V} of positive real numbers such that (x; y)∈E ⇔ |Ix∩ Iy|¿min{ x; y}. We show that every tolerance graph has a polynomial size integer representation. It follows that tolerance graph recognition is in NP. c © 2004 Elsevier B.V. All rights reserved.

Let G=(V, E) be an Eulerian graph embedded on a triangulizable surface S. We show that E can be decomposed into closed curves C1 , ..., Ck such that mincr(G, D)= i=1 mincr(Ci , D) for each closed curve D on S. Here mincr(G, D) denotes the minimum number of intersections of G and D$ (counting multiplicities), where D$ ranges over all closed curves D$ freely homotopic to D and not intersecting V....