Graph Neural Networks (GNNs) have been widely used in various graph-based applications. Recent studies shown that GNNs are vulnerable to link-level membership inference attacks (LMIA) which can infer whether a given link was included the training graph of GNN model. While most focus on privacy vulnerability links entire graph, none inspected risk specific subgroups (e.g., between LGBT users). I...

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the ...

The graphs play an important role in our daily life. For example, the urban transport network can be represented by a graph, as the intersections are the vertices and the streets are the edges of the graph. Suppose that some edges of the graph are removed, the question arises, how damaged the graph is. There are some criteria for measuring the vulnerability of graph; the...

‎A set of vertices $S$ of a graph $G$ is called a fixing set of $G$‎, ‎if only the trivial automorphism of $G$ fixes every vertex in $S$‎. ‎The fixing number of a graph is the smallest cardinality of a fixing‎ ‎set‎. ‎The fixed number of a graph $G$ is the minimum $k$‎, ‎such that ‎every $k$-set of vertices of $G$ is a fixing set of $G$‎. ‎A graph $G$‎ ‎is called a $k$-fixed graph‎, ‎if its fix...

Graph similarity computation aims to predict a score between one pair of graphs facilitate downstream applications, such as finding the most similar chemical compounds query compound or Fewshot 3D Action Recognition. Recently, some graph models based on neural networks have been proposed, which are either graph-level interaction node-level comparison. However, when number nodes in increases, it...

Techniques for global register allocation via graph coloring have been extensively studied and widely implemented in compiler frameworks. This paper examines a particular variant – the Callahan Koblenz allocator – and compares it to the Chaitin-Briggs graph coloring register allocator. Both algorithms were published in the 1990’s, yet the academic literature does not contain an assessment of th...

Economic theory suggests that liberalization of trade between countries with differing levels of environmental protection could lead pollution-intensive industry to concentrate in the nations where regulations are lax. This effect, often referred to as the “pollution haven” hypothesis, is much discussed in theory, but finds only ambiguous support in empirical research to date. Methodologies use...

We introduce the notion of a conformal design based on a vertex operator algebra. This notation is a natural analog of the notion of block designs or spherical designs when the elements of the design are based on self-orthogonal binary codes or integral lattices, respectively. It is shown that the subspaces of fixed degree of an extremal self-dual vertex operator algebra form conformal 11-, 7-,...

People with disabilities have the same fundamental right to access mainstream services in the community (education, health-care, employment, social services and social protection) as any other citizen. Inclusive transport is a critical element in a comprehensive strategy of mainstreaming people with disabilities in developing countries. A freely accessible society without any physical obstacles...

‎a set $s$ of vertices of a graph $g=(v,e)$ without isolated vertex‎ ‎is a {em total dominating set} if every vertex of $v(g)$ is‎ ‎adjacent to some vertex in $s$‎. ‎the {em total domatic number} of‎ ‎a graph $g$ is the maximum number of total dominating sets into‎ ‎which the vertex set of $g$ can be partitioned‎. ‎we show that the‎ ‎total domatic number of a random $r$-regular graph is almost‎...