20.500.12556/RUL-190888 Combinatorial aspects of the nonsymmetric strong spectral property for graphs In this paper, we investigate the nonsymmetric strong spectral property (nSSP) from a combinatorial perspective. To zero–nonzero patterns of matrices, we associate directed graphs and study when they require or allow the nSSP, providing a framework that avoids verifying the nSSP for individual matrices. A new combinatorial method is introduced and used to recognize several patterns that require the nSSP. It is shown that loop assignments in double paths play a critical role in establishing this property. In particular, we characterize all possible loop assignments for double paths on at most five vertices that require, allow or do not allow the nSSP, and show that an open question regarding irreducible tridiagonal patterns has a negative answer. We also investigate whether the minimum number of arcs in a directed graph on n vertices that requires the nSSP, is equal to 2n − 1, and confirm this minimum for several specific digraph families. nonsymmetric strong spectral property nSSP sign pattern matrices digraphs inverse eigenvalue problem nesimetrična krepka spektralna lastnost nSSP predznačeni vzorci matrik usmerjeni grafi inverzni problem lastnih vrednosti true false true Angleški jezik Slovenski jezik Članek v reviji 2026-11-06 10:42:34 2026-11-06 10:42:36 2026-11-07 04:23:19 0000-00-00 00:00:00 2026 0 0 Str. 755-779 Vol. 42 Sep. 2026 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 0000-00-00 512.643:519.17 1537-9582 10.13001/ela.2026.10523 304180483 Combinatorial_aspects_of_Koljancic_Oblak_2026.pdf Combinatorial_aspects_of_Koljancic_Oblak_2026.pdf 1 F9AEF5066D3B170EBDFD24C8A27B9386 5cffb38bd0b94cb2d231ac3a182598c43c9eff423e71b454e5b486670380c0ab 362cacf1-d9c7-11f1-aea2-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=252668 https://journals.uwyo.edu/index.php/ela/article/view/10523 1 53426b99-d9c6-11f1-aea2-0050569b8976 https://repozitorij.uni-lj.si/Dokument.php?lang=slv&id=252667 Fakulteta za računalništvo in informatiko 0 0 0