In a graph G with a given edge colouring, a rainbow path is a path all of whose edges have distinct colours. The minimum number of colours required to colour the edges of G so that every pair of vertices is joined by at least one rainbow path is called the rainbow connection number rc(G) of the graph G. For any graph G, rc(G) > diam(G). We will show that for the Erdős–Rényi random graph G(n, p)...

The Rainbow Signature Scheme is a non-trivial generalization of the well known Unbalanced Oil and Vinegar Signature Scheme (Eurocrypt '99) minimizing the length of the signatures. Recently a new variant based on non-commutative rings, called NC-Rainbow, was introduced at CT-RSA 2012 to further minimize the secret key size. We disprove the claim that NC-Rainbow is as secure as Rainbow in general...

A tree T , in an edge-colored graph G, is called a rainbow tree if no two edges of T are assigned the same color. A k-rainbow coloring of G is an edge coloring of G having the property that for every set S of k vertices of G, there exists a rainbow tree T in G such that S ⊆ V (T ). The minimum number of colors needed in a k-rainbow coloring of G is the k-rainbow index of G, denoted by rxk(G). G...

Abstract In this study, we investigate the collapsing scenario for k- essence emergent Vaidya spacetime in context of massive gravity's rainbow. For consider that background metric is We show gravity closely resembles new type generalized with rainbow deformations null fluid collapse, where scalar field as a function solely advanced or retarded time. The mass also different. This satisfies requ...

Let G be an edge-colored copy of Kn, where each color appears on at most n/2 edges (the edgecoloring is not necessarily proper). A rainbow spanning tree is a spanning tree of G where each edge has a different color. Brualdi and Hollingsworth [4] conjectured that every properly edge-colored Kn (n ≥ 6 and even) using exactly n−1 colors has n/2 edge-disjoint rainbow spanning trees, and they proved...

we define minimal cn-dominating graph $mathbf {mcn}(g)$, commonality minimal cn-dominating graph $mathbf {cmcn}(g)$ and vertex minimal cn-dominating graph $mathbf {m_{v}cn}(g)$, characterizations are given for graph $g$ for which the newly defined graphs are connected. further serval new results are developed relating to these graphs.

A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by γt. The maximal size of an inclusionwise minimal total dominating set, the upper total domination num...

Rainbow is a Java and web-based distributed database system designed for academic purposes, and serves as an exercise to understand concepts of distributed transactions and transaction management including concurrency control, atomic actions, data replication, and fault tolerance. The motivation for the Rainbow project is twofold. First, Rainbow can be used as a teaching tool. Graduate students...

the objective of this study was to compare growth performance and feed conversion ratios of rainbow trout (oncorhynchus mykiss) and brook trout (salvelinus fontinalis) juveniles in monoculture and duo-culture in freshwater and seawater under aquarium conditions. the fish were about 2-months old hatchery-reared brook and rainbow trout with initial weights of 0.934±0.033 (n=360) and 1.014±0.019 (...