A characterization of graphs with supereulerian line graphs. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Huang, Yufei; He, Weihua; Huang, Guixian; Lai, Hong-Jian; Song, Sulin
• Is Part Of: International journal of computer mathematics. Volume 5:Issue 1(2020)
• Page Start: 1
• Page End: 14
• Publication Date: 2020-01-02
• Subjects: Eulerian -- supereulerian -- line graph -- collapsible graph -- trail; Computer systems -- Periodicals; Computer systems; Periodicals; 004
• DOI: 10.1080/23799927.2019.1708465
• Languages: English
• ISSNs: 2379-9927

Abstract

Abstract : The line graph L ( G ) of a graph G is a simple graph with E ( G ) being its vertex set, where two vertices are adjacent in L ( G ) whenever the corresponding edges share a common vertex in G . A graph H is even if every vertex of H has even degree, and a graph is supereulerian if it has a spanning closed trail. We obtain a characterization for a graph G to have a supereulerian line graph L ( G ), as follows: for a connected graph G with | E ( G ) | ≥ 3, the line graph L ( G ) has a spanning closed trail if and only if G has an even subgraph H (possibly null) such that both G remains connected after deleting all degree 2 vertices not in H, and every degree 2 vertex not in H must be adjacent only to vertices of degree at least 3 in G .