ABOUT THE MAXIMUM NUMBER OF VERTICES IN PRIMITIVE REGULAR GRAPHS WITH EXPONENT EQUALS 3

Some results on the maximum number of vertices in primitive regular graphs with exponent 3 are presented. We have found upper bound of this number depending on the degree p: np 6 p 3 − p 2 − 3p + 5. Also, the exact value of the maximum number of vertices in primitive cubic graphs with exponent 3 is given: n3 = 12. A computation experiment has been conducted, and we have found the number of primitive regular graphs with degree p 6 9, number of vertices n 6 16 and exponent 3 for each (n, p) pair.