Oriented unicyclic graphs with minimal skew Randić energy

Authors

  • Wei Gao Penn State Abington
  • Yanling Shao North University of China

DOI:

https://doi.org/10.11575/cdm.v16i3.71273

Abstract

Let GG be a simple graph with vertex set V(G)={v1,v2, ,vn}, and Gσ be an orientation of G. Denote by d(vi) the degree of the vertex vi for i=1,2,,n. The skew Randić matrix of Gσ, denoted by RS(Gσ), is the real skew-symmetric matrix (rij)n×n, where rij=1/d(vi)d(vj) and rji=1/d(vi)d(vj) if vivj is an arc of Gσ, otherwise rij=rji=0. The skew Randi\'{c} energy RES(Gσ) of Gσ is defined as the sum of the norms of all the eigenvalues of RS(Gσ). In this paper, the oriented unicyclic graphs with minimal skew Randić energy are determined.

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Published

2021-12-31

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Section

Articles