Strong geodetic problem on Cartesian products of graphs
Iršič, Vesna, 1993- ; Klavžar, Sandi
Krepko geodetski problem je nedavna inačica geodetskega problema. Za graf ▫$G$▫ je njegovo krepko geodetsko število ▫$\text{sg}(G)$▫ kardinalnost najmanjše podmnožice vozlišč ▫$S$▫, da vsako vozlišče ...▫$G$▫ leži na eni fiksni najkrajši poti med dvema vozliščema iz ▫$S$▫. V tem članku je obravnavan krepki geodetski problem na kartezičnem produktu grafov. Določena je splošna zgornja meja za ▫$\text{sg}(G \,\square\, H)$▫ in tudi vrednosti za ▫$K_m \,\square\, K_n$▫, ▫$K_{1, k} \,\square\, P_l$▫ in prizme nad ▫$K_n-e$▫. Obravnavana je tudi povezava med krepkim geodetskim številom grafa in krepkim geodetskim številom njegovih podgrafov.
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