We present a survey of results on the edge disjoint paths problem and re late this problem to the edge disjoint homotopic path and the edge disjoint homotopic cycle problem The latter problem is given a graph G V E embedded on a surface S and closed curves C Ck on S nd necessary and su cient conditions for the existence of pairwise edge disjoint cycles e C e Ck in G so that e Ci is homotopic to...

A graph G is collapsible if for every even subset X ~ V(G), G has a subgraph r such that G E(J ') is connected and the set of odd-degree vertices of J' is X. A graph obtained by contracting all the non-trivial collapsible subgraphs of G is called the reduction of G. In this paper. we characterize graphs of diameter two in terms of collapsible subgraphs and investigate the relationship between t...

For the terminology and notations not defined here, we adopt those in Bondy and Murty [1] and Xu [2] and consider simple graphs only. Let G = (V,E) be a graph with vertex set V = V (G) and edge set E = E(G). For any vertex v ∈ V , NG(v) denotes the open neighborhood of v in G and NG[v] = NG(v) ∪ {v} the closed one. dG(v) = |NG(v)| is called the degree of v in G, ∆ and δ denote the maximum degre...

R. Devi, A. Selvakumar and M. Parimala, αψ-closed sets in Topological spaces (Submitted). Y. Kucuk, On some characterizations of δ-continuous multifunctions, Demonstratio Math., Vol 28(3)(1995), 587-595. P. E. Long and L. L. Herrington, The τθ topology and faintly continuous functions, Kyungpook Math. J., 22(1982), 7-14. T. Noiri and V. Popa, Almost weakly continuous multifunctions, Demon-strat...

Abstract A multilevel distance labeling of the graph G is a function f = (V (G),E(G)) on V (G) of G into N ∪ {0} so that |f(u) − f(v)| ≥ diam(G) + 1− d(u, v) for all u, v ∈ V (G). The smallest span taken over all multilevel distance labeling of G is radio number rn(G) of G. In this paper, we completely determine the radio number rn(G) of G where G is the graph obtained from generalized Petersen...

An exponential dominating set of graph $G = (V,E )$ is a subset $Ssubseteq V(G)$ such that $sum_{uin S}(1/2)^{overline{d}{(u,v)-1}}geq 1$ for every vertex $v$ in $V(G)-S$, where $overline{d}(u,v)$ is the distance between vertices $u in S$ and $v  in V(G)-S$ in the graph $G -(S-{u})$. The exponential domination number, $gamma_{e}(G)$, is the smallest cardinality of an exponential dominating set....

Domination and 2-domination numbers are defined only for graphs with non-isolated vertices. In a Graph G = (V, E) each vertex is said to dominate every in its closed neighborhood. graph G, subset S of V(G) called 2-dominating set if v ∈ V, V-S has atleast two neighbors S. The smallest cardinality known as the number γ2(G). this paper, we find some special also graphs.

in the present paper, we study some properties of fuzzy norm of linear operators. at first the bounded inverse theorem on fuzzy normed linear spaces is investigated. then, we prove hahn banach theorem, uniform boundedness theorem and closed graph theorem on fuzzy normed linear spaces. finally the set of all compact operators on these spaces is studied.

An assignment of integer numbers to the vertices of a given graph under certain conditions is referred to as a graph labeling. The assignment of labels from the set {0,1,2,...,2 1} q to the vertices of G (with ( ) G n V vertices and ( ) q E G edges) such that, when each edge has assigned a label defined by the absolute difference of its end-points, the resulting edge labels are 1,3 ,2 1 q is re...

It has been shown [Balister, 2001] that if n is odd and m1, . . . , mt are integers with mi ≥ 3 and ∑t i=1 mi = |E(Kn)| then Kn can be decomposed as an edge-disjoint union of closed trails of lengths m1, . . . , mt. Here we show that the corresponding result is also true for any sufficiently large and sufficiently dense even graph G.