On Eulerian Irregularities of Prisms, Grids and Powers of Cycles

Eric Andrews1, Chira Lumduanhom1, Ping Zhang1
1Department of Mathematics Western Michigan University Kalamazoo, MI 49008-5248, USA

Abstract

For a nontrivial connected graph \(G\), an Eulerian walk in \(G\) is a closed walk that contains every edge of \(G\) at least once. An Eulerian walk is irregular if it encounters no two edges of \(G\) the same number of times and the minimum length of an irregular Eulerian walk in \(G\) is the Eulerian irregularity of \(G\). In this work, we determine the Eulerian irregularities of all prisms, grids and powers of cycles.

Keywords: Eulerian walk and irregularity, prism, grid, powers of cycles. AMS Subject Classification: 05C38, 05C45.