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This is the Moore graph, which is a regular graph of degree $d$ with diameter $k$, with maximum possible nodes. A calculation shows that the number of nodes $n$ is at leastmost

$$1+d \sum_{i=0}^{k-1} (d-1)^i$$

and as you mentioned it can be shown by spectral techniques that the only possible values for $d$ are

$$d = 2,3,7,57.$$

Example for $d=7$ is the Hoffmanâ€“Singleton graph, but for the case $d=57$ it is still open. See Theorem 8.1.5 in the book "Spectra of graphs" by Brouwer and Haemers for reference.

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This is the Moore graph, which is a regular graph of degree $d$ with diameter $k$, with maximum possible nodes. A calculation shows that the number of nodes $n$ is at least

$$1+d \sum_{i=0}^{k-1} (d-1)^i$$

and as you mentioned it can be shown by spectral techniques that the only possible values for $d$ are

$$d = 2,3,7,57.$$

Example for $d=7$ is the Hoffmanâ€“Singleton graph, but for the case $d=57$ it is still open. See Theorem 8.1.5 in the book "Spectra of graphs" by Brouwer and Haemers for reference.

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This is the Moore graph, which is a regular graph of degree $d$ with diameter $k$, with maximum possible nodes. A calculation shows that the number of nodes $n$ is at least

$$1+d \sum_{i=0}^{k-1} (d-1)^i$$

and as you mentioned it can be shown by spectral techniques that the only possible values for $d$ are

$$d = 2,3,7,57.$$

Example for $d=7$ is the Hoffmanâ€“Singleton graph, but for the case $d=57$ it is still open. See Theorem 8.1.5 in the book "Spectra of graphs" by Brouwer and Haemers for reference.