@article{Article_99,

title = {Weighted digraphs having exactly two nonzero skew eigenvalues},

journal = {Communications in Combinatorics, Cryptography & Computer Science},

volume = {2025},

issue = {1},

issn = { 2783-5456 },

year = {2026},

url = {http://cccs.sgh.ac.ir/Articles/2025/issue 1/1-3-Weighteddigraphshavingexactlytwononzeroskeweigenvalues.pdf},

author = {Harishchandra S. Ramane and K. C. Nandeesh and Medha Itagi-Huilgol},

keywords = {Digraph, skew matrix, eigenvalues.},

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.}

};