Geodesic
On the local structure of distance-regular Mathon graphs
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 293-298 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the structure of local subgraphs of distance-regular Mathon graphs of even valency. We describe some infinite series of locally $\Delta$-graphs of this family, where $\Delta$ is a strongly regular graph that is the union of affine polar graphs of type "$-$," a pseudogeometric graph for $pG_{l}(s,l)$, or a graph of rank 3 realizable by means of the van Lint-Schrijver scheme. We show that some Mathon graphs are characterizable by their intersection arrays in the class of vertex transitive graphs.
Keywords: arc-transitive graph, distance-regular graph, (locally) strongly regular graph
Mots-clés : antipodal cover, Mathon graph, automorphism. 
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L. Yu. Tsiovkina. On the local structure of distance-regular Mathon graphs. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 293-298. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a30/

[1] Makhnev A.A., Paduchikh D.V., Tsiovkina L.Yu., “Reberno simmetrichnye distantsionno regulyarnye nakrytiya klik s $\lambda=\mu$”, Tr. In-ta matematiki i mekhaniki UrO RAN, 19:2 (2013), 237–246 | MR

[2] Makhnev A.A., “Chastichnye geometrii i ikh rasshireniya”, Uspekhi mat. nauk, 54:5(329) (1999), 25–76 | DOI | MR | Zbl

[3] Makhnev A.A., Samoilenko M.S., “O distantsionno regulyarnykh nakrytiyakh klik s silno regulyarnymi okrestnostyami vershin”, Sovr. probl. matem. i ee pril., sb. tr. 46-i Mezhdunar. mol. shk.-konf., IMM UrO RAN, Ekaterinburg, 2015, 13–18

[4] Brouwer A.E., Cohen A.M., Neumaier A., Distance-regular graphs, Springer-Verlag, Berlin etc, 1989, 494 pp. | MR | Zbl

[5] Godsil C.D., Liebler R.A., Praeger C.E., “Antipodal distance transitive covers of complete graphs”, Europ. J. Comb., 19:4 (1998), 455–478 | DOI | MR | Zbl

[6] Dickson L.E., Linear groups: with an exposition of the Galois field theory, Dover Publications, N. Y., 1958 | MR | Zbl

[7] Kleidman P.B., Liebeck W.M., The subgroup structure of the finite classical groups, London Math. Soc. Lect. Notes Texts, 129, Cambr. Univ. Press, Cambridge, 1990, 304 pp. | MR | Zbl

[8] Shrijver A., van Lint J.H., “Construction of strongly regular graphs, two-weight codes and partial geometries by finite fields”, Combinatorica, 1 (1981), 63–73 | DOI | MR

[9] Suzuki M., “On a class of doubly transitive groups”, Ann. of Math. (2), 75:1 (1962), 105–145 | DOI | MR | Zbl

[10] Tsiovkina L.Yu., “Two new infinite families of arc-transitive antipodal distance-regular graphs of diameter three with $\lambda=\mu$ related to groups $Sz(q)$ and $^2G_2(q)$”, J. Algebr. Comb., 41 (2015), 1079–1087 | DOI | MR | Zbl