3 problems

Let $egr(v,k,g,\lambda)$ denote an edge-girth-regular graph with $v$ vertices, valency $k$, girth $g$, and each edge contained in exactly $\lambda$ cycles of length $g$. Let…

Higher-girth existence conjecture. For $q\geq 3$ a prime power and $g\in\{8,12\}$, there exists a family of

The edge-girth conjecture. The family of graphs $\mathcal G_q(V,E)$ is a family of