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New largest graphs of diameter 6. (Extended Abstract)

- Pineda-Villavicencio, Guillermo, Gomez, Jose, Miller, Mirka, Pérez-Rosés, Hebert

**Authors:**Pineda-Villavicencio, Guillermo , Gomez, Jose , Miller, Mirka , Pérez-Rosés, Hebert**Date:**2006**Type:**Text , Journal article**Relation:**Electronic Notes in Discrete Mathematics Vol. 24, no. (2006), p. 153-160**Full Text:****Reviewed:****Description:**In the pursuit of obtaining largest graphs of given degree and diameter, many construction techniques have arisen. Compounding of graphs is one such technique. In this paper, by means of the compounding of complete graphs into the bipartite Moore graph of diameter 6, we obtain two families of (**Description:**C1

On bipartite graphs of diameter 3 and defect 2

- Delorme, Charles, Jorgensen, Leif, Miller, Mirka, Pineda-Villavicencio, Guillermo

**Authors:**Delorme, Charles , Jorgensen, Leif , Miller, Mirka , Pineda-Villavicencio, Guillermo**Date:**2009**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 61, no. 4 (2009), p. 271-288**Full Text:****Reviewed:****Description:**We consider bipartite graphs of degree A<2, diameter D = 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (â–³,3, -2) -graphs. We prove the uniqueness of the known bipartite (3, 3, -2) -graph and bipartite (4, 3, -2)-graph. We also prove several necessary conditions for the existence of bipartite (â–³,3, -2) - graphs. The most general of these conditions is that either â–³ or â–³-2 must be a perfect square. Furthermore, in some cases for which the condition holds, in particular, when â–³ = 6 and â–³ = 9, we prove the non-existence of the corresponding bipartite (â–³,3,-2)-graphs, thus establishing that there are no bipartite (â–³,3, -2)-graphs, for 5

**Authors:**Delorme, Charles , Jorgensen, Leif , Miller, Mirka , Pineda-Villavicencio, Guillermo**Date:**2009**Type:**Text , Journal article**Relation:**Journal of Graph Theory Vol. 61, no. 4 (2009), p. 271-288**Full Text:****Reviewed:****Description:**We consider bipartite graphs of degree A<2, diameter D = 3, and defect 2 (having 2 vertices less than the bipartite Moore bound). Such graphs are called bipartite (â–³,3, -2) -graphs. We prove the uniqueness of the known bipartite (3, 3, -2) -graph and bipartite (4, 3, -2)-graph. We also prove several necessary conditions for the existence of bipartite (â–³,3, -2) - graphs. The most general of these conditions is that either â–³ or â–³-2 must be a perfect square. Furthermore, in some cases for which the condition holds, in particular, when â–³ = 6 and â–³ = 9, we prove the non-existence of the corresponding bipartite (â–³,3,-2)-graphs, thus establishing that there are no bipartite (â–³,3, -2)-graphs, for 5

New largest known graphs of diameter 6

- Pineda-Villavicencio, Guillermo, Gómez, José, Miller, Mirka, Pérez-Rosés, Hebert

**Authors:**Pineda-Villavicencio, Guillermo , Gómez, José , Miller, Mirka , Pérez-Rosés, Hebert**Date:**2009**Type:**Text , Journal article**Relation:**Networks Vol. 53, no. 4 (2009), p. 315-328**Full Text:****Reviewed:****Description:**In the pursuit of obtaining largest graphs of given maximum degree**Description:**2003007890

**Authors:**Pineda-Villavicencio, Guillermo , Gómez, José , Miller, Mirka , Pérez-Rosés, Hebert**Date:**2009**Type:**Text , Journal article**Relation:**Networks Vol. 53, no. 4 (2009), p. 315-328**Full Text:****Reviewed:****Description:**In the pursuit of obtaining largest graphs of given maximum degree**Description:**2003007890

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