Families of small regular graphs of girth 7Report as inadecuate



 Families of small regular graphs of girth 7


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The first known families of cages arised from the incidence graphs of generalized polygons of order $q$, $q$ a prime power. In particular, $(q+1,6)$-cages have been obtained from the projective planes of order $q$. Morever, infinite families of small regular graphs of girth 5 have been constructed performing algebraic operations on $\mathbb{F} q$. In this paper, we introduce some combinatorial operations to construct new infinite families of small regular graphs of girth 7 from the $(q+1,8)$-cages arising from the generalized quadrangles of order $q$, $q$ a prime power.



Author: M. Abreu; G. Araujo-Pardo; C. Balbuena; D. Labbate; J. Salas

Source: https://archive.org/







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