International Journal of Mathematics and Mathematical Sciences
Volume 1 (1978), Issue 2, Pages 177-185
Graphs which have pancyclic complements
Department of Mathematics, SUNY College at Fredonla, Fredonla 14063, New York, USA
Received 23 January 1978; Revised 1 March 1978
Copyright © 1978 H. Joseph Straight. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let and denote the number of vertices and edges of a graph , respectively. Let denote the maximum degree of , and the complement of . A graph of order is said to be pancyclic if contains a cycle of each length , . For a nonnegative integer , a connected graph is said to be of rank if . (For equal to and these graphs are called trees and unicyclic graphs, respectively.)
In 1975, I posed the following problem: Given , find the smallest positive integer , if it exists, such that whenever is a rank graph of order and then is pancyclic. In this paper it is shown that a result by Schmeichel and Hakiml (2) guarantees that exists. It is further shown that for , , and , , , and , respectively.