A survivable path (W,P ) between a pair of vertices xi, xj in undirected simple graph G is an ordered pair of edge-disjoint simple paths consisting of a working path W = xi...xj and a protection path P = xi...xj . An optimal set of survivable paths in graph G corresponds to a set of mesh-restored lightpaths defined on an optical network that minimizes the number of used optical channels. In thi...

altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. we now provide a generalization of the altan concept, applicable to any graph. several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. among these ar...

let g be a (p,q) graph. an injective map f : e(g) → {±1,±2,...,±q} is said to be an edge pair sum labeling if the induced vertex function f*: v (g) → z - {0} defined by f*(v) = σp∈ev f (e) is one-one where ev denotes the set of edges in g that are incident with a vertex 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} according a...

We present a series of experimental designs based on different mesh survivability principles and study how the working and spare capacity requirements of each network type vary with the network average nodal degree or notionally, the connectivity of the facilities graph of the network. This is accompanied by an attempt at some simple theories for bounding or estimating how capacity and redundan...

Privacy is one of the major concerns when publishing or sharing social network data for social science research and business analysis. This paper is motivated by the recognition of the need for a finer grain and personalized privacy in data publication of social netwoks.Recently , researchers have proposed a privacy protection scheme that not only prevents the disclosure of identity of users bu...

This paper is based on the Network security situation awareness. It describes the framework designed to generate security graph. The proposed framework is easy to install and provides protection against denial of service and distributed denial of service attacks. It also displays security analysis of the sensors attached to the network

Let G(V, E) be an undirected connected graph, where each vertex v is associated with a positive cost C(v) and each edge e 5 (u, v) is associated with two positive weights, W(u! v) and W(v! u). We consider a new graph problem, called the edge-orientation problem (the EOP). The major issue is to assign each edge e 5 (u, v) an orientation, either from u to v, denoted as u! v, or from v to u, denot...

This paper is motivated by the recognition of the need for a finer grain and more personalized privacy in data publication of social networks. We propose a privacy protection scheme that not only prevents the disclosure of identity of users but also the disclosure of selected features in users’ profiles. An individual user can select which features of her profile she wishes to conceal. The soci...

Recommender systems have become prosperous nowadays, designed to predict users’ potential interests in items by learning embeddings. Recent developments of the Graph Neural Networks (GNNs) also provide recommender (RSs) with powerful backbones learn embeddings from a user-item graph. However, only leveraging interactions suffers cold-start issue due difficulty data collection. Hence, current en...

a emph{signed graph} (or, in short, emph{sigraph}) $s=(s^u,sigma)$ consists of an underlying graph $s^u :=g=(v,e)$ and a function $sigma:e(s^u)longrightarrow {+,-}$, called the signature of $s$. a emph{marking} of $s$ is a function $mu:v(s)longrightarrow {+,-}$. the emph{canonical marking} of a signed graph $s$, denoted $mu_sigma$, is given as $$mu_sigma(v) := prod_{vwin e(s)}sigma(vw).$$the li...