A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...

A preferential attachment model for a growing network incorporating deletion of edges is studied and the expected asymptotic degree distribution is analyzed. At each time step t = 1, 2, . . ., with probability π1 > 0 a new vertex with one edge attached to it is added to the network and the edge is connected to an existing vertex chosen proportionally to its degree, with probability π2 a vertex ...

We present a randomized algorithm for dynamic graph connectivity. With failure probability less than 1/n (for any constant c we choose), our solution has worst case running time O(log n) per edge insertion, O(log n) per edge deletion, and O(log n/ log log n) per query, where n is the number of vertices. The previous best algorithm has worst case running time O(log n) per edge insertion and O(lo...

Reachability queries are of great importance in many research and application areas, including general graph mining, social network analysis and so on. Many approaches have been proposed to compute whether there exists one path from one node to another node in a graph. Most of these approaches focus on static graphs, however in practice dynamic graphs are more common. In this paper, we focus on...

A connected graph is said to be super edge-connected if every minimum edge-cut isolates a vertex. The restricted edge-connectivity λ′ of a connected graph is the minimum number of edges whose deletion results in a disconnected graph such that each connected component has at least two vertices. A graph G is called λ′-optimal if λ′(G) = min{dG(u)+dG(v)−2 : uv is an edge in G}. This paper proves t...

Let $t$ be a positive real number. A graph is called \emph{$t$-tough} if the removal of any vertex set $S$ that disconnects leaves at most $|S|/t$ components. The toughness largest for which $t$-tough. minimally $t$-tough and deletion edge from decreases toughness. \emph{chordal} it does not contain an induced cycle length least $4$. We characterize $t$-tough, chordal graphs all $t\le 1/2$. As ...

For graphs H and F, the generalized Turán number ex(n,H,F) is largest of copies in an F-free graph on n vertices. We say that F-Turán-good if (χ(F)−1)-partite graph, provided large enough. present a general theorem case F has edge whose deletion decreases chromatic number. In particular, this determines ex(n,Pk,C2ℓ+1) ex(n,C2k,C2ℓ+1) exactly, also study when vertex

‎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 ...

This paper deals with the facility location problems balancing on allocation clients to servers. Two bi-objective models are considered, in which one objective is traditional p-median or p-maxian and second minimize maximum demand volume allocated any facility. An edge deletion method time complexity O(n^2) presented for balanced $2$-median problem a tree. For 2-maxian problem, it shown optimal...