Graph theory and its applications

By Steve Abbott. Mathematical Gazette, 2000

911 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/2956d522a42758a687ce629c3053d658b429d828

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In Computational Theory and Mathematics

Citations in the corpus

Formation control: a review and a new consideration (2005, background): “There are rich literatures on graph theory, what we present here is based on [19], [20], [21].”
The pond network: can structural connectivity reflect on (amphibian) biodiversity patterns? (2011, positive): “…taken from its original mathematical context and is nowadays applied to many diverse disciplines (computer sciences, social sciences, etc.) (e.g. Gross and Yellen 2006), including understanding biological process as food webs, community stability and gene and protein networks (Proulx et al.…”
A survey of graph theoretical approaches to image segmentation (2013, methodology): “After each iteration, the vertices in the Dijkstra tree are those to which the shortest paths from s have been found [86].”
Technologies for 3D mesh compression: A survey (2005, background): “More rigorous definitions can be found in [10] [11] [12].”
Landscape connectivity: A conservation application of graph theory (2000, background): “It is primarily concerned with maximally efficient flow or connectivity in networks (Gross and Yellen, 1999).”
Pregel: a system for large-scale graph processing (2010, methodology): “This algorithm may perform many more comparisons than sequential counterparts such as Dijkstra or Bellman-Ford [5, 15, 17, 24 ], but it is able to solve the shortest paths problem at a scale that is infeasible with any single-machine implementation.”
On the Maximum Zagreb Indices of Graphs with k Cut Vertices (2010, methodology): “In our exposition we will use the terminology and apparatus of (chemical) graph theory (see [7, 10, 53]).”
CONNECTIVITY, FRAGMENTATION, AND EXTINCTION RISK IN DENDRITIC METAPOPULATIONS (2002, background): “For convenience, I explore the consequences of varying the number of patches by reference to the dimensions of bifurcating dendritic networks (complete binary trees in the terminology of graph theory [Gross and Yellen 1999]) whose tree depth (the number of ''levels'' of patches, Fig.”
Λ scattering equations (2016, methodology): “We choose the left and right base as7 in figure 32, such that the diagrams in the (LIL) and (RIR) vectors have a Hamiltonian decomposition [58, 59].”
Prime Cordial Labeling of Some Graphs (2012, neutral): “To investigate similar results for other graph fam es as well as in the context of different labeling problems is an open area of research. nW ti p 8n g of th 13W es ili REFERENCES [1] J. Gross and J. Yellen, “Graph Theory and Its Applications,” CRC Press, Boca Raton, 1999.”
Supply network disruption and resilience: A network structural perspective (2015, background): “the World Wide Web, power grids, and food webs (Gross and Yellen, 2006; Newman, 2010).”
A Laplacian Framework for Option Discovery in Reinforcement Learning (2017, background): “Matrix T is known as the incidence matrix (Gross & Yellen, 2006).”
Dual-Primal Graph Convolutional Networks (2018, background): “We brieﬂy summarize the properties of dual graphs and refer the reader to [19, 18, 16] P O E is the maximum vertex out-degree in the primal graph (if G is undirected d max = max i =1 ,...,n d i should be considered instead of d outmax ).”
Transit functions on graphs (and posets) (2007, background): “For a slightly different notion of betweenness, see [30].”
Old and new results on algebraic connectivity of graphs (2007, background): “For more details, see Gross and Yellen [35].”
A brief survey on anonymization techniques for privacy preserving publishing of social network data (2008, background): “The graph construction problem is related to the problem of realizing degree sequence with constraints, which has been studied extensively in graph theory [7, 16].”
Relational Pooling for Graph Representations (2019, background): “These highly symmetric graphs are instances of circulant graphs and are well-known in the graph theory literature (Sethuraman, 2004).”