Inverse Problems in Graph Theory: Nets
A. A. Makhnev , M. P. Golubyatnikov , Wenbin Guo
Communications in Mathematics and Statistics ›› 2019, Vol. 7 ›› Issue (1) : 69 -83.
Inverse Problems in Graph Theory: Nets
Let $\varGamma $ be a distance-regular graph of diameter 3 with strong regular graph $\varGamma _3$. The determination of the parameters $\varGamma _3$ over the intersection array of the graph $\varGamma $ is a direct problem. Finding an intersection array of the graph $\varGamma $ with respect to the parameters $\varGamma _3$ is an inverse problem. Previously, inverse problems were solved for $\varGamma _3$ by Makhnev and Nirova. In this paper, we study the intersection arrays of distance-regular graph $\varGamma $ of diameter 3, for which the graph ${\bar{\varGamma }}_3$ is a pseudo-geometric graph of the net $PG_{m}(n, m)$. New infinite series of admissible intersection arrays for these graphs are found. We also investigate the automorphisms of distance-regular graph with the intersection array $\{20,16,5; 1,1,16 \}$.
Distance-regular graph / Pseudo-geometric graph / Strong regular graph
/
| 〈 |
|
〉 |