Topic
Voltage graph
About: Voltage graph is a research topic. Over the lifetime, 8292 publications have been published within this topic receiving 236232 citations.
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13 Jul 1987TL;DR: Introduction Voltage graphs and Covering Spaces Surfaces and Graph Imbeddings Imbedded Voltage Graphs and Current Graphs Map Colorings The Genus of A Group References.
Abstract: Introduction Voltage Graphs and Covering Spaces Surfaces and Graph Imbeddings Imbedded Voltage Graphs and Current Graphs Map Colorings The Genus of A Group References.
1,542 citations
01 Feb 1997
TL;DR: The double-pushout approach to graph transformation, which was invented in the early 1970's, is introduced in the Handbook of Graph Grammars and Computing by Graph.
Abstract: A graph program consists of declarations of conditional graph transformation rules G. Rozenberg, editors: Handbook of Graph Grammars and Computing. We introduce s-graph grammars, a new grammar formalism for computing Handbook of Graph Grammars and Computing by Graph Transformation, pp. The double-pushout approach to graph transformation, which was invented in the early 1970's, is Handbook of Graph Grammars and Computing by Graph.
1,366 citations
TL;DR: This work determines the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree and presents an algorithm with polynomially bounded (but exponential in k) worst case time complexity.
Abstract: A k-tree is a graph that can be reduced to the k-complete graph by a sequence of removals of a degree k vertex with completely connected neighbors. We address the problem of determining whether a graph is a partial graph of a k-tree. This problem is motivated by the existence of polynomial time algorithms for many combinatorial problems on graphs when the graph is constrained to be a partial k-tree for fixed k. These algorithms have practical applications in areas such as reliability, concurrent broadcasting and evaluation of queries in a relational database system. We determine the complexity status of two problems related to finding the smallest number k such that a given graph is a partial k-tree. First, the corresponding decision problem is NP-complete. Second, for a fixed (predetermined) value of k, we present an algorithm with polynomially bounded (but exponential in k) worst case time complexity. Previously, this problem had only been solved for $k = 1,2,3$.
1,350 citations
TL;DR: This survey overviews the definitions and methods for graph clustering, that is, finding sets of ''related'' vertices in graphs, and presents global algorithms for producing a clustering for the entire vertex set of an input graph.
1,329 citations