logo_acta

Acta Mathematica Vietnamica

A CHARACTERIZATION OF SOME CUBIC (m,n)-METACIRCULANT GRAPHS

icon-email NGO DAC TAN

Abstract

It has been proved in [5] that if a graph G is isomorphic to a cubic (m,n)-metacirculant graph MC(m,n,α,S0,S1,,Sμ) with S0, then G is isomorphic to either a union of finitely many disjoint copies of a circulant graph C(2,S), where >1 and S={1,1,} or a union of finitely many disjoint copies of a generalized Petersen graph GP(d,k), where d>2 and k2±1 (mod d). In this paper, we prove that the converse is also true.