Locally constrained graph homomorphisms—structure, complexity, and applications

Locally constrained graph homomorphisms - structure, complexity, and applications

A graph homomorphism is an edge preserving vertex mapping between two graphs. Locally constrained homomorphisms are those that behave well on the neighborhoods of vertices — if the neighborhood of any vertex of the source graph is mapped bijectively (injectively, surjectively) to the neighborhood of its image in the target graph, the homomorphism is called locally bijective (injective, surjecti...

Locally constrained graph homomorphisms and equitable partitions

We explore the connection between locally constrained graph homomorphisms and degree matrices arising from an equitable partition of a graph. We provide several equivalent characterizations of degree matrices. As a consequence we can efficiently check whether a given matrix M is a degree matrix of some graph and also compute the size of a smallest graph for which it is a degree matrix in polyno...

Graph Convexity Parameters: Complexity and Applications

Applications of Graph Operations

In this paper, some applications of our earlier results in working with chemical graphs are presented.

Constrained locally weighted clustering

Data clustering is a difficult problem due to the complex and heterogeneous natures of multidimensional data. To improve clustering accuracy, we propose a scheme to capture the local correlation structures: associate each cluster with an independent weighting vector and embed it in the subspace spanned by an adaptive combination of the dimensions. Our clustering algorithm takes advantage of the...