Let k be an integer and M be a closed 2-manifold with Euler characteristic χ(M) ≤ 0. We prove that each polyhedral map G on M with minimum degree δ and large number of vertices contains a k-path P , a path on k vertices, such that: (i) for δ ≥ 4 every vertex of P has, in G, degree bounded from above by 6k − 12, k ≥ 8 (It is also shown that this bound is tight for k even and that for k odd this ...

Let G = (V, E) be a simple graph with p vertices and q edges. For connected of diameter d, radio mean labeling is one to mapping f from V(G) N satisfying the condition for every μ, ν ∈ V (G). The span maximum integer that maps vertex G. number G, rmn(G) lowest taken over all labelings In this paper, we analyze some splitting graphs labeling.

This paper presents two novel sorting network-based architectures for computing high sample rate non-recursive rank order lters. The proposed architectures consist of signiicantly fewer comparators than existing sorting network-based architectures that are based on bubble-sort and Batcher's odd-even merge sort. The reduction in the number of comparators is obtained by sorting the columns of the...

We address the problem of sorting a large number N of keys on a MasPar MP-1 parallel SIMD machine of moderate size P where the processing elements (PEs) are interconnected as a toroidal mesh and have 16KB local storage each. We present a comparative study of implementations of the following deterministic oblivious sorting methods: Bitonic Sort, Odd-Even Merge Sort, and FastSort. We successfully...

Sorting data is an important problem for many applications. Parallel sorting is a way to improve sorting performance using more nodes or threads e.g. dividing data in more nodes and perform sorting in each node simultaneously or including more threads in process of sorting. It was experimented with one type of those sorting algorithms, namely the well-known sorting algorithms called Odd-Even so...

let $a$ be a non-trivial abelian group and $a^{*}=asetminus {0}$. a graph $g$ is said to be $a$-magic graph if there exists a labeling$l:e(g)rightarrow a^{*}$ such that the induced vertex labeling$l^{+}:v(g)rightarrow a$, define by $$l^+(v)=sum_{uvin e(g)} l(uv)$$ is a constant map.the set of all constant integerssuch that $sum_{uin n(v)} l(uv)=c$, for each $vin n(v)$,where $n(v)$ denotes the s...

An L(h,k)-labeling of a graph G is an assignment non-negative integers to the vertices such that if two u and v are adjacent then they receive labels differ by at least h, when not but there two-hop path between them, k. The span λ labeling difference largest smallest vertex assigned. Let λhk ( )denote admits L(h,k) -labeling using from {0,1,...λ}. A Cayley group called circulant order n, isomo...

Girth pairs were introduced by Harary and Kovács [Regular graphs with given girth pair, J. Graph Theory 7 (1983) 209–218]. The odd girth (even girth) of a graph is the length of a shortest odd (even) cycle. Let g denote the smaller of the odd and even girths, and let h denote the larger. Then (g, h) is called the girth pair of the graph. In this paper we prove that a graph with girth pair (g, h...

The antibandwidth problem is to label vertices of a n-vertex graph injectively by 1, 2, 3, . . . n, so that the minimum difference between labels of adjacent vertices is maximised. The problem is motivated by the obnoxious facility location problem, radiocolouring, work and game scheduling and is dual to the well known bandwidth problem. We prove exact results for the antibandwidth of complete ...