5-regular oriented graphs with optimum skew energy

Lifeng Guo, Ligong Wang, Peng Xiao

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Let G be a simple undirected graph and Gσ be the corresponding oriented graph of G with the orientation σ. The skew energy of Gσ, denoted by εs(Gσ), is defined as the sum of the singular values of the skew adjacency matrix S(Gσ). In 2010, Adiga et al. certified that ɛs(Gσ)≤nΔ, where Δ is the maximum degree of G of order n. It has been shown that every 5-regular oriented graph with optimum skew energy has even neighborhood property, that is each pair of neighborhoods of a graph have even number of common vertices. In this paper, we characterize all connected 5-regular graphs of order n with this property. Moreover, we determine all connected 5-regular oriented graphs of order n with maximum skew-energy.

Original languageEnglish
Pages (from-to)43-59
Number of pages17
JournalApplied Mathematics and Computation
Volume301
DOIs
StatePublished - 15 May 2017

Keywords

  • Oriented graph
  • Skew energy
  • Skew-adjacency matrix

Fingerprint

Dive into the research topics of '5-regular oriented graphs with optimum skew energy'. Together they form a unique fingerprint.

Cite this