an injective map f : e(g) → {±1, ±2, · · · , ±q} is said to be an edge pair sum labeling of a graph g(p, q) if the induced vertex function f*: v (g) → z − {0} defined by f*(v) = (sigma e∈ev) f (e) is one-one, where ev denotes the set of edges in g that are incident with a vetex v and f*(v (g)) is either of the form {±k1, ±k2, · · · , ±kp/2} or {±k1, ±k2, · · · , ±k(p−1)/2} u {k(p+1)/2} accordin...

A graph is locally connected if for each vertex v of degree --2, the subgraph induced by the vertices adjacent to v is connected . In this paper we establish a sharp threshold function for local connectivity . Specifically, if the probability of an edge of a labeled graph of order n is p = ((3/2 + s„) log n/n)'/ 2 where s„ _ ( log log n + log(3/8) + 2x)/(2 log n), then the limiting probability ...

The constant rate birth-death process is a popular null model for speciation and extinction. If one removes extinct and non-sampled lineages, this process induces 'reconstructed trees' which describe the relationship between extant lineages. We derive the probability density of the length of a randomly chosen pendant edge in a reconstructed tree. For the special case of a pure-birth process wit...

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An ex...

This paper considers the minimum spanning tree (MST) problem in the Congested Clique model and presents an algorithm that runs in O(log log log n) rounds, with high probability. Prior to this, the fastest MST algorithm in this model was a deterministic algorithm due to Lotker et al. (SIAM J on Comp, 2005) from about a decade ago. A key step along the way to designing this MST algorithm is a con...

An edge may be defined as a set of connected pixels that forms a boundary between two disjoints regions. Edge detection is basically, a method of segmenting an image into regions of discontinuity. Edge detection plays an important role in digital image processing and practical aspects of our life. .In this paper we studied various edge detection techniques as Prewitt, Robert, Sobel, Marr Hildri...

A random graph model with prescribed degree distribution and degree dependent edge weights is introduced. Each vertex is independently equipped with a random number of half-edges and each half-edge is assigned an integer valued weight according to a distribution that is allowed to depend on the degree of its vertex. Half-edges with the same weight are then paired randomly to create edges. An ex...

We derive sharp thresholds for exact recovery of communities in a weighted stochastic block model, where observations are collected in the form of a weighted adjacency matrix, and the weight of each edge is generated independently from a distribution determined by the community membership of its endpoints. Our main result, characterizing the precise boundary between success and failure of maxim...

‎let $g$ be a graph and $chi^{prime}_{aa}(g)$ denotes the minimum number of colors required for an‎ ‎acyclic edge coloring of $g$ in which no two adjacent vertices are incident to edges colored with the same set of colors‎. ‎we prove a general bound for $chi^{prime}_{aa}(gsquare h)$ for any two graphs $g$ and $h$‎. ‎we also determine‎ ‎exact value of this parameter for the cartesian product of ...