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On Distance Induced Seidel Matrices for Signed Graphs | ||
| Communications in Combinatorics and Optimization | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 17 تیر 1404 | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2025.30248.2382 | ||
| نویسندگان | ||
| Biju K1، 2؛ Shahul Hameed Koombail* 3 | ||
| 1Department of Mathematics, P R N S S College, Mattannur, Kannur, Kerala, India | ||
| 2Research Scholar, Dr. Hermann Gundert Central Library and Research Centre, Kannur University, Kerala, India | ||
| 3Principal(Retired), Government Arts and Science College, Uduma, Kasaragod 671318 | ||
| چکیده | ||
| A signed graph $\Sigma=(G,\sigma)$ is a graph $G$ together with a signature function $\sigma$ which assigns $1$ or $-1$ on the edges of $G$. Seidel matrix of an unsigned graph is already defined and researchers investigated some of its spectral and other properties. Considering the recently introduced notion of signed distance in signed graphs and that of the distance compatible signed graphs, we define distance induced Seidel matrices for such signed graphs and analyze their spectrum mainly for some classes of unbalanced distance compatible signed graphs, as balanced signed graphs possess the same distance induced Seidel spectrum as that of its underlying graph. We also deal with the distance compatibility issue in the line graph of a distance compatible signed graph and discuss the corresponding distance induced Seidel spectrum in this regard. | ||
| کلیدواژهها | ||
| Signed graphs؛ Distance compatibility؛ Adjacency Matrix؛ Vertex-edge orientation؛ Line graph | ||
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