On growing connected β -skeletons

Adamatzky, 2008, Developing proximity graphs by physarum polycephalum: Does the plasmodium follow Toussaint hierarchy?, Parallel Process. Lett., 19, 105, 10.1142/S0129626409000109 Adamatzky, 2010 2012 A. Adamatzky, How β-skeletons lose their edges, 2012, submitted for publication. Amenta, 1998, The crust and the β-skeleton: Combinatorial curve reconstruction, Graph. Models Image Process., 60, 125, 10.1006/gmip.1998.0465 Billiot Dale, 2000 Dale, 2002, Conceptual and mathematical relationships among methods for spatial analysis, Ecography, 25, 558, 10.1034/j.1600-0587.2002.250506.x Delaunay, 1934, Sur la sphère vide, Izv. Akad. Nauk SSSR, Otd. Mat. Estestv. Nauk, 7, 793 Estrada, 2001, Generalization of topological indices, Chem. Phys. Lett., 336, 248, 10.1016/S0009-2614(01)00127-0 Estrada, 2002, The structural interpretation of the Randić index, Internet Electron. J. Mol. Des., 1, 360 Gabriel, 1969, A new statistical approach to geographic variation analysis, Syst. Zool., 18, 259, 10.2307/2412323 Golding, 1998, Studies of bacterial branching growth using reaction–diffusion models for colonial development, Phys. A, 260, 510, 10.1016/S0378-4371(98)00345-8 Hall, 1975, Molecular connectivity. II. Relationship to water solubility and boiling point, J. Pharm. Sci., 64, 1974, 10.1002/jps.2600641215 Jaromczyk, 1992, Relative neighborhood graphs and their relatives, Proc. IEEE, 80, 1502, 10.1109/5.163414 Jombart, 2008, Revealing cryptic spatial patterns in genetic variability by a new multivariate method, Heredity, 101, 92, 10.1038/hdy.2008.34 Kier, 1975, Molecular connectivity. I. Relationship to nonspecific local anesthesia, J. Pharm. Sci., 64, 1971, 10.1002/jps.2600641214 Kier, 1976 Kirkpatrick, 1985, A framework for computational morphology, 217 Legendre, 1989, Spatial pattern and ecological analysis, Vegetatio, 80, 107, 10.1007/BF00048036 Li, 2004, Application of computation geometry in wireless networks, 197 Li, 2008, An updated survey on the Randić index, Math. Chem. Monogr., 6, 9 Magwene, 2008, Using correlation proximity graphs to study phenotypic integration, Evol. Biol., 35, 191, 10.1007/s11692-008-9030-y Matula, 1980, Properties of Gabriel graphs relevant to geographic variation research and clustering of points in the plane, Geogr. Anal., 12, 205, 10.1111/j.1538-4632.1980.tb00031.x Muhammad, 2007, A distributed graph algorithm for geometric routing in ad hoc wireless networks, J. Networks, 2, 49, 10.4304/jnw.2.6.50-57 Randić, 1975, Characterization of molecular branching, J. Am. Chem. Soc., 97, 6609, 10.1021/ja00856a001 Runions, 2005, Modeling and visualization of leaf venation patterns, ACM Trans. Graph., 24, 702, 10.1145/1073204.1073251 Sabljić, 1982, Molecular connectivity: A novel method for prediction of bioconcentration factor of hazardous chemicals, Chem.-Biol. Interact., 42, 301, 10.1016/0009-2797(82)90074-6 Santi, 2005 Sokal, 2008, Spatial autocorrelation in biology 1. Methodology, Biol. J. Linn. Soc., 10, 199, 10.1111/j.1095-8312.1978.tb00013.x W.-Z. Song, Y. Wang, X.-Y. Li, Localized algorithms for energy efficient topology in wireless ad hoc networks, in: Proc. MobiHoc 2004, Roppongi, Japan, May 24–26, 2004. Sridharan, 2010, Gabriel graph of geomagnetic Sq variations, Acta Geophys., 58, 973, 10.2478/s11600-010-0004-y Toroczkai, 2007, Proximity networks and epidemics, Phys. A, 378, 68, 10.1016/j.physa.2006.11.088 Wan, 2007, On the longest edge of Gabriel graphs in wireless ad hoc networks, IEEE Trans. Parallel Distrib. Syst., 18, 111, 10.1109/TPDS.2007.253285 Watanabe, 2005, A study on analyzing the road network pattern using proximity graphs, J. City Plann. Inst. Japan, 40, 133, 10.11361/journalcpij.40.3.133 Watanabe, 2008, Evaluating the configuration and the travel efficiency on proximity graphs as transportation networks, Forma, 23, 81