Let p be a singularity of a normal two–dimensional analytic surface X. In general π : M → X will denote a resolution of (X, p), and A = π(p). It is well–known that the dual resolution graph of the germ (X, p) determines the topology of the germ (X, p). Indeed, the (real) link of (X, p) can be reconstructed from the resolution graph as a plumbing. Conversely, by a result of W. Neumann [15], the ...

Recently, the authors introduced a game invariant of graphs, called connectivity. In this paper, we investigate edge version invariant, edge-connectivity, by introducing new combinatorial on graph, graph edge-cutting game. The is one generalizations classical game, named Shannon switching As an analog study have complete characterization graphs with edge-connectivity infinity in terms number ed...

Let G be a finite graph and A be a subgraph of Aut(G). We give a necessary and sufficient condition for the graph G to have an A-invariant spanning tree.

We introduce a graph invariant, called thinness, and show that a maximum weighted stable set on a graph G(V;E) with thinness k may be found in O( jV j

We present a general notion of properties that are characterized by local conditions that are invariant under a sufficiently rich class of symmetries. Our framework generalizes two popular models of testing graph properties as well as the algebraic invariances studied by Kaufman and Sudan (STOC’08). Our focus is on the case that the property is characterized by a constant number of local condit...

It is an important task to learn a representation for images which has low dimension and preserve the valuable information in original space. At the perspective of manifold, this is conduct by using a series of local invariant mapping. Inspired by the recent successes of deep architectures, we propose a local invariant deep nonlinear mapping algorithm, called graph regularized auto-encoder (GAE...

Graph isomorphism problem is to determine whether two given graphs are isomorphic. It is a particular type of a more general problem “the isomorphism of incidence system”. I propose some new invariants for heuristic search of graph isomorphism and demonstrate that they are really useful in practice by experiments. Keyword. graph isomorphism, graph invariant, graph spectrum , adjacency matrix, m...

The metric dimension of a graph is the size of the smallest set of vertices whose distances distinguish all pairs of vertices in the graph. We show that this graph invariant may be calculated by an algorithm whose running time is linear in the input graph size, added to a function of the largest possible number of leaves in a spanning tree of the graph.

Graph Isomorphism is a widely studied problem due to its practical applications in various fields of networks, chemistry and finger print detection, recent problems in biology such as diabetes detection, protein structure and information retrieval. An approach to the graph isomorphism detection is based on vertex invariant. In the existing approach vertex invariants is used to partition the mat...