Original Research Article

Article volume = 2025 and issue = 1

Pages: 35–39

Article publication Date: June 30, 2026

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Weighted digraphs having exactly two nonzero skew eigenvalues

Harishchandra S. Ramane(a,∗), K. C. Nandeesh(b), Medha Itagi-Huilgol(c)

(a) Department of Mathematics, Karnatak University, Dharwad - 580003, India

(b) Department of Mathematics, Karnataka State Open University, Mysuru - 570006, India

(c) Department of Mathematics, Dr. Manmohan Singh Bengaluru City University, Bengaluru - 560001, India

Abstract:

The matrix with respect to the real n-vector a = [a1, a2, . . . , an]T is an n × n matrix M(a) = [mij], where mij = ai − aj. The weighted digraph Da with vertex set V(G) = {v1, v2, . . . , vn} indexed with the vector a is obtained by drawing an arc of weight ai − aj from vi to vj if ai − aj > 0. If the vector a has at least two distinct elements, then M(a) has exactly two non zero eigenvalues. Further we discuss the structural properties of Da.

Keywords:

Digraph, skew matrix, eigenvalues.

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Cite this article as:
  • Harishchandra S. Ramane, K. C. Nandeesh, Medha Itagi-Huilgol, Weighted digraphs having exactly two nonzero skew eigenvalues, Communications in Combinatorics, Cryptography & Computer Science, 2025(1), PP.35–39, 2026
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