An odd graceful labeling of a graph ( , ) G V E = is a function : ( ) {0,1,2, . . .2 ( ) 1} f V G E G → − such that | ( ) ( )| f u f v − is odd value less than or equal to 2 ( ) 1 E G − for any , ( ) u v V G ∈ . In spite of the large number of papers published on the subject of graph labeling, there are few algorithms to be used by researchers to gracefully label graphs. This work provides gene...

Graceful degradation is critical ability of highly available middleware such as a web application server but naive graceful degradation is often unsatisfactory. If a web application server provides multiple services under heavy workload, it must gracefully degrade the execution performance of each service to a different degree depending on the quality required to that service. This paper reveal...

System-wide graceful degradation may be a viable approach to improving dependability in computer systems. In order to evaluate and improve system-wide graceful degradation we present initial work on a component-based model that will explicitly define graceful degradation as a system property, and measure how well a system gracefully degrades in the presence of multiple combinations of component...

System-wide graceful degradation may be a viable approach to improving dependability in computer systems. In order to evaluate and improve system-wide graceful degradation we present a system model that will explicitly define graceful degradation as a system property, and measure how well a system gracefully degrades in the presence of multiple combinations of component failures. The system’s s...

Complex programs are often required to display graceful degradation, reacting adaptively to changes in the environment. Under ideal circumstances, the program's behavior satisfies a set of application-dependent constraints. In the presence of events such as failures, timing anomalies, synchronization conflicts, or security breaches, certain constraints may become difficult or impossible to sati...

A graph labeling is an assignment of integers to the vertices (or) edges or both subject to certain conditions. Graceful labeling was introduced by Rosa [6] while the concept of odd graceful labeling was introduced by Gnanajothi [2]. A Graph G (V, E), |V(G)| = p, |E(G)| = q is said to be odd graceful if there is an injection from V(G) to {0, 1, 2, .... 2q-1} such that when each edge xy is assig...

The efficient distribution of stored information has become a major concern in the Internet. Since the web workload characteristics shows that more than 60% of network traffic is caused by image documents, how to efficiently distribute image documents from servers to end clients is an important issue. Proxy cache is an efficient solution to reduce network traffic. And it has been shown that an ...

In this paper we have further elaborated MPLS multicasting under the specific graph (graceful) labeling with the use of specific multicast tree topology called caterpillar which is next higher topological structure other than the path; that is a central concept in the IP unicast routing. The use of caterpillar as the multicast tree has been analyzed and compared with the other tree topologies u...

For a simple path Pr on r vertices, the square of Pr is the graph P 2 r on the same set of vertices of Pr, and where every pair of vertices of distance 2 or less in Pr are connected by an edge. Given a (p, q)-graph G with p vertices and q edges, and an integer k ≥ 0, G is said to be k-edge-graceful if the edges can be labeled by k, k+1, . . . , k+q−1 so that the induced vertex sums (mod p) are ...