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There are many interesting questions one can ask about a highly symmetric graph.
A graph with a transitive automorphism group can be obtained starting with a group
G and a small set S of generators....
Expander Graph Based Overlapped Chunked Codes
Expander Graph Based Overlapped Chunked Codes
2012/12/4
Chunked codes are a variation of random linear network codes with low computational complexities. In chunked codes, the packets in a file are grouped into small (non-overlapped or overlapped) chunks, ...
Computing the obstacle number of a plane graph
obstacle number of a plane graph Computational Geometry
2011/10/9
Abstract: An obstacle representation of a plane graph G is V(G) together with a set of opaque polygonal obstacles such that G is the visibility graph on V(G) determined by the obstacles. We investigat...
Rigidity of high dimensional graph manifolds
Quasi-isometry quasi-action graph of groups CAT(0) space Borel conjecture Baum-Connes conjecture
2011/9/1
Abstract: We define the class of high dimensional graph manifolds. These are compact smooth manifolds supporting a decomposition into finitely many pieces, each of which is diffeomorphic to the produc...
Degree conditions for the partition of a graph into triangles and quadrilaterals
degree partition triangle quadrilateral
2011/3/1
For two positive integers r and s with r ≥ 2s−2, if G is a graph of order 3r+4s such that d(x)+d(y) ≥ 4r+4s for every xy 6∈ E(G), then G independently contains r triangles and s quadrilaterals, ...
Edge Growth in Graph Cubes
Edge Growth Graph Cubes
2010/11/29
We show that for every connected graph G of diameter 3, the graph G3 has average degree 7
4(G). We also provide an example showing that this bound is best possible. This resolves a question of H...
Sum of Squares of Degrees in a Graph
Graph Degree sequence Threshold graph Pell's Equation Partition Density
2010/4/16
Let be the set of all simple graphs with vertices and edges and let denote the sum of the squares of the degrees, , of the vertices of . It is known that the maximum value of for occurs at on...
Application of Tree-like Structure of Graph to Matrix Analysis
Application Tree-like Structure Matrix Analysis
2010/11/1
Formulas for matrix determinants, algebraic adjunctions, characteristic polynomial coefficients, components of eigenvectors are obtained in the form of signless sums of matrix elements products taking...
Some Graph Type Hypersurfaces in a Semi-Euclidean Space
graph lightlike hypersurface minimal semi-Euclidean space totally geodesic
2010/3/1
We consider some graph type hypersurfaces in a semi-Euclidean space \Bbb Rn+1q and give conditions of the dimension n+1 and the index q when a hypersurface is lightlike, totally geodesic and minimal.