The term graceful degradation describes the smooth change to a lower state of some system aspect as a response to the occurrence of an event that prohibits the manifestation of the fully fledged system behavior. Graceful degradation has appeared in a variety of domains, from image processing and telecommunications to shared memory multiprocessors and multi-modular memory systems. In each domain...

In this paper some new type of odd graceful graphs are investigated. We prove that the graph obtained by joining a cycle C8 with some star graphs S1,r keeping one vertex and three vertices gap between pair of vertices of the cycle admits odd graceful labelling. We also prove that the graph obtained by joining a cycle C12 with some star graphs S1,r keeping two, three and five vertices gap betwee...

By strengthening an edge-decomposition technique for gracefully labelling a generalised Petersen graph, we provide graceful labellings for a new infinite family of such graphs. The method seems flexible enough to provide graceful labellings for many other classes of graphs in the future.

Abstract E-super arithmetic graceful labelling of a graph G is bijection f from the union vertex set and edge to positive integers (1, 2, 3, … |V(G) ∪ E(G)|) such that edges have labels {1, …, |E(G)|} induced mapping * given by (uv) = f(u) + f(v) − f(uv) for uv ∈ E(G) has range {|V(G) E(G)| 1, |V(G)| 2|E(G)|} In this paper we prove H i (m, m) (1) chain even cycles C 4,n , 6,n are graceful.

The graceful exit transition from a dilaton-driven inflationary phase to a decelerated Friedmann−Robertson−Walker era requires certain classical and quantum corrections to the string effective action. Classical corrections can stabilize a high curvature string phase while the evolution is still in the weakly coupled regime, and quantum corrections can induce violation of the null energy conditi...

We discuss the possibility of a smooth transition from the pre-to the post-big bang regime, in the context of the lowest-order string eeective action (without higher-derivative corrections), taking into account with a phenomenological model of source the repulsive gravitational eeects due to the back-reaction of the quantum uctuations outside the horizon. We determine a set of necessary conditi...

We propose the model of Chain Inflation, in which a sequential chain of coupled scalar fields drives inflation. Motivated by the stringy landscape, we allow the number of fields to be very large, ranging from hundreds to many more; we note that the model is quite general and applies to any multidimensional potential, in string theory or otherwise. Each stage of inflation (which can be thought o...

mean labelings are a type of additive vertex labeling. this labeling assigns non-negative integers to the vertices of a graph in such a way that all edge-weights are different, where the weight of an edge is defined as the mean of the end-vertex labels rounded up to the nearest integer. in this paper we focus on mean labelings of some graphs that are the result of the corona operation. in parti...

For a defined graph labeling, there exists a number of bijective functions for a graph of defined order and size which leads to different graphs. In this paper, a mathematical tool is developed to find the number of super vertex graceful graphs for a defined order “p” and size “q”. Mathematics Subject Classification: 05C78