Small Regular Graphs of Girth 7
نویسندگان
چکیده
In this paper, we construct new infinite families of regular graphs of girth 7 of smallest order known so far. Our constructions are based on combinatorial and geometric properties of (q + 1, 8)-cages, for q a prime power. We remove vertices from such cages and add matchings among the vertices of minimum degree to achieve regularity in the new graphs. We obtain (q + 1)-regular graphs of girth 7 and order 2q3 + q2 + 2q for each even prime power q > 4, and of order 2q3 + 2q2 − q + 1 for each odd prime power q > 5.
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ورودعنوان ژورنال:
- Electr. J. Comb.
دوره 22 شماره
صفحات -
تاریخ انتشار 2015