Showing papers on "Path graph published in 1970"
24 citations
TL;DR: For each d such that d -1 is prime, a d -valent graph of girth 6 having 2(d 2 − d + 1) vertices was exhibited in this article.
10 citations
TL;DR: In this article, the necessary and sufficient conditions for a sequence of positive integers to be the power sequence of a connected graph on n vertices with m edges are given, and the class of all extremal graphs is determined.
Abstract: Necessary and sufficient conditions for a sequence (p
1,p
2, …,p
n
) of positive integers to be the power sequence of a connected graph onn vertices withm edges are given. The maximum power of a connected graph onn vertices withm edges and the class of all extremal graphs are also determined.
TL;DR: In this paper, it was shown that by using vertex matrices and a path inversion-induced duality between paths and loops, the work of finding additional graph formulas from a given formula can often be reduced.
Abstract: Through use of vertex matrices and a path inversion-induced duality between paths and loops, it is shown that the work of finding additional graph formulas from a given formula can often be reduced.