Let A be a non-trivial, finitely-generated abelian group and A∗ = A\{0}. A graph is A-magic if there exists an edge labeling using elements of A∗ which induces a constant vertex labeling of the graph. In this paper, we analyze the group-magic property for complete n-partite graphs and composition graphs with deleted edges.

We consider the family of graph problems called node-deletion problems, defined as follows: For a fixed graph property l7, what is the minimum number of nodes which must be deleted from a given graph so that the resulting subgraph satisfies l7? We show that if l7 is nontrivial and hereditary on induced subgraphs, then the node-deletion problem for n is NP-complete for both undirected and direct...

As a generalization of the traditional connectivity, g -component edge connectivity c ? ( G ) non-complete graph is minimum number edges to be deleted from such that resulting has at least components. Hypercube-like networks (HL-networks for short) are obtained by manipulating some pairs in hypercubes, which contain several famous interconnection as twisted cubes, Möbius crossed locally cubes. ...

Intruders often combine exploits against multiple vulnerabilities in order to break into the system. Each attack scenario is a sequence of exploits launched by an intruder that leads to an undesirable state such as access to a database, service disruption, etc. The collection of possible attack scenarios in a computer network can be represented by a directed graph, called network attack gra...

By mapping the vertices of a graph G to points in ℝ3, and its edges corresponding line segments, we obtain three-dimensional realization G. A is said be globally rigid if edge lengths uniquely determine realization, up congruence. The called every generic rigid. We consider global rigidity properties braced triangulations, which are graphs obtained from maximal planar by adding extra edges, bra...

In this paper we present an algorithmic approach to packing A-paths. It is regarded as a generalization of Edmonds’ matching algorithm, however there is the significant difference that here we do not build up any kind of alternating tree. Instead we use the so-called 3-way lemma, which either provides augmentation, or a dual, or a subgraph which can be used for contraction. The method works in ...

In this paper we reconstruct nontrivial connected Cartesian product graphs from single vertex deleted subgraphs. We show that all one-vertex extensions of a given connected graph H, nite or innnite, to a nontrivial Cartesian product are isomorphic.