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On an Algorithm for Ordering of Graphs

Published online by Cambridge University Press:  20 November 2018

Milan Sekanina
Milan Sekanina*
Affiliation:
University of Manitoba, Winnipeg, Manitoba; University of J. E. Purkyně, Brno, Czechoslovakia
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Let (G, ρ) be a finite connected (undirected) graph without loops and multiple edges. So x, y being two elements of G (vertices of the graph (G, ρ)), 〈x, y〉 ∊ ρ means that x and y are connected by an edge. Two vertices x, y ∊ G have the distance μ(x, y) equal to n, if n is the smallest number with the following property: there exists a sequence x0, x1, …, xn of vertices such that x0 = x, xn = y and 〈xi-1, Xi〉 ∊ ρ for i = 1, …, n. If x ∊ G, we put μ(x, x) = 0.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 2 , June 1971 , pp. 221 - 224
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Sekanina, Milan, On an ordering of the set of vertices of a connected graph, Publ. Fac. Sci. Univ. Brno, No. 412 (1960), 137-142.Google Scholar
2. Karaganis, J., On the cube of a graph, Canad. Math. Bull. 11 (1968), 295-296.Google Scholar
3. Chartrand, G. and Kapoor, S. F., The cube of every connected graph is 1-Hamiltonian, J. Res. Nat. Bur. Standards Sect. B. 73B (1969), 47-48.Google Scholar