An r-dynamic coloring of a graph G is proper c the vertices such that |c(N(v))| ≥ min {r, d(v)}, for each v ∈ V(G). The chromatic number minimum k has an with colors. In this paper, we obtain δ-dynamic central vertex join two graphs.

We consider superfluous elements in a bounded lattice with 0 and 1, introduce various types of graphs associated these elements. The notions such as element graph (S(L)), join intersection (JI(L)) lattice, distributive (SI(L)) are defined. Dual atoms play an important role to find connections between the lattice-theoretic properties those corresponding graph-theoretic properties. Consequently, ...

A fuzzy graph can be obtained from two given fuzzy graphs using union and join. In this paper, we find the degree of an edge in fuzzy graphs formed by these operations in terms of the degree of edges in the given fuzzy graphs in some particular cases. 1. Introduction Fuzzy graph theory was introduced by Azriel Rosenfeld in 1975 [4]. Though it is very young, it has been growing fast and has nume...

The join operation, which combines tuples from multiple relations, is the most fundamental and, typically, the most expensive operation in database queries. The standard approach to join-query optimization is cost based, which requires developing a cost model, assigning an estimated cost to each queryprocessing plan, and searching in the space of all plans for a plan of minimal cost. Two other ...

For a graph G, let χ(G) and λ(G) denote the chromatic number of G and the maximum local edge connectivity of G, respectively. A result of Dirac implies that every graph G satisfies χ(G) 6 λ(G) + 1. In this paper we characterize the graphs G for which χ(G) = λ(G) + 1. The case λ(G) = 3 was already solved by Aboulker, Brettell, Havet, Marx, and Trotignon. We show that a graph G with λ(G) = k > 4 ...

Let G be a k-degenerate graph of order n. It is well-known that G has no more edges than Sn,k, the join of a complete graph of order k and an independent set of order n−k. In this note, it is shown that Sn,k is extremal for some spectral parameters of G as well. More precisely, letting μ (H) and q (H) denote the largest eigenvalues of the adjacency matrix and the signless Laplacian of a graph H...

In this paper we propose NNCTPH, a new MapReduce algorithm that is able to build an approximate k-NN graph from large text datasets. The algorithm uses a modified version of Context Triggered Piecewise Hashing to bin the input data into buckets, and uses an exhaustive search inside the buckets to build the graph. It also uses multiple stages to join the different unconnected subgraphs. We exper...

A new type of decomposition of graphs – the operator decomposition connected with the classical notion of homogeneous set (or module) is introduced. The properties of this decomposition are described. Using this decomposition we prove the following. Let P and Q be two hereditary graph classes such that P is closed with respect to the operation of join and Q is closed with respect to the operati...

We prove that perfect graphs with no balanced skew-partitions admits a O(n) Clique-Stable set separator. We then prove that for every graph G in this class, there always exists two subsets of vertices V1, V2 such that |V1|, |V2| ≥ c|V (G)| for some constant c and V1 is either complete or anticomplete to V2. The method uses trigraphs, introduced by Chudnovsky [5], and relies on the good behavior...