20 problems

Maximum subgraph conjecture. If $U$ spans a complete subgraph or an empty subgraph of order $q$ in $V_q$, then $U$ is a line in $F_q\times F_q$.

Let $q$ be a prime power, and let the collinearity graph of the polar space $\mathcal{Q}^{-}(5,q)$ be the graph whose vertices are the points of $\mathcal{Q}^{-}(5,q)$, with two ve…

Let $\Gamma$ be a graph as in Hypothesis; in particular, $\Gamma$ is a strongly-regular graph in the setting of the paper. Complete classification conjecture. The graph $\Gamma$ is…

Let $G$ be a connected $k$-regular graph with $n$ vertices and co-edge-regular with parameter $\mu$, having four distinct eigenvalues. Let $t\geq 2$ be an integer. Tan et al.'s con…

Cohn–de Laat–Leijenhorst conjecture. Three-point semidefinite programming bounds prove that $C$ is a maximal spherical code.

Uniquely $C_{4}^{+}$-saturation conjecture. A graph $G$ is nontrivial uniquely $C_{4}^{+}$-saturated if and only if $G$ is a strongly regular graph with parameters $(n,k,0,2)$ or…

Let $G$ be a strongly regular graph with parameters $\lambda=1$ and $\mu=2$, order $n$, and valency $k$. Let $p_6$ denote the number of hexagons in $G$. Exact hexagon-count conject…

Koolen–Gebremichel conjecture. Either $\mu\in\{6,9\}$ or $n\leqslant 276$.

Faudree–Rousseau–Sheehan's conjecture. There exists a constant $c\ge2$ such that for every strongly regular graph $srg(\nu,k,\lambda,\mu)$,

Let $G=(V,E)$ be a strongly regular conference graph with parameters … where $\beta\geq 2$. The condensed Ricci curvature conjecture. The condensed Ricci curvature satisfies … for…

A strongly regular graph (SRG) $G$ with parameters $(n,k,\lambda,\mu)$ is a $k$-regular graph on $n$ vertices such that every adjacent pair has exactly $\lambda$ common neighbors a…

Let $q=p^{\ell}$ be a prime power, let $m$ be a positive integer, and let $N$ divide $(q^m-1)/(q-1)$. Let $C_0^{(N,q^m)}$ be the subgroup of $\mathbb{F}_{q^m}^*$ of index $N$, and…

Let $\Gamma$ be a connected co-edge-regular graph with four distinct eigenvalues. Let $t\geq 2$ be an integer and write $|V(\Gamma)|=n(\Gamma)$. An $s$-clique extension is a graph…

Emms–Hancock–Severini–Wilson conjecture.

Let $G$ be a graph on $n$ vertices, let $\overline G$ be its complement, and let $s^+(G)$ denote the sum of the squares of the positive adjacency eigenvalues. A conference graph is…

Let $G=(V,E)$ be a strongly regular graph. Its girth is the length of its shortest cycle; in particular, girth $3$ means that $G$ contains a triangle. Strongly regular girth-three…

Let $p>2$ and let $f:GF(p)^n\to GF(p)$ be a weakly regular bent function corresponding to a weighted strongly regular graph via the stated analogy. Let $\mu_{ii}$ denote the diagon…

Strong regularity conjecture. For even dimension $m$, the graph of integral distances $\mathfrak{G}_{m,q}$ is a strongly regular graph. The conjecture predicts that the common-neig…

Let $G$ be a connected $(v,k,\lambda,\mu)$-strongly regular graph, and let $S$ be a disconnecting set of $G$ whose removal disconnects $G$ into non-singleton components. Brouwer's…

Let $G$ and $H$ be strongly regular graphs with the same set of parameters. For a graph $F$, let ${\bf U}(F)$ denote its transition matrix, let ${\bf U}(F)^3$ be its third power, l…