Welcome to the resource topic for
**2022/1489**

**Title:**

New results on algebraic graphs of large girth and their impact on Extremal Graph Theory and Algebraic Cryptography

**Authors:**
Vasyl Ustimenko

**Abstract:**

For arbitrary finite field F_q, q > 2 we prove that known qregular bipartite algebraic graphs A(n; q) existence on 2q^n vertices have

girth 2n or 2n + 2. Similar result is formulated for more general graphs

A(n; K) defined over general commutative integrity ring K. The impact

of these results on Extremal Graph Theory and graph based Algebraic

Cryptography is discussed.

**ePrint:**
https://eprint.iacr.org/2022/1489

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