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13.
Weights on edges of chemical graphs determined by paths
Pisanski, Tomaž ; Žerovnik, Janez, 1958-
V članku priredimo uteži povezavam grafa na dva načina. S ▫$P$▫ oziroma ▫$(P^\ast)$▫ označimo pot (najkrajšo pot) med točkama ▫$a$▫ in ▫$b$▫, z ▫$n(a,b)$▫ ▫$(n^\ast (a,b))$▫ pa število poti ...(najkrajših poti) med ▫$a$▫ in ▫$b$▫. Uteži definiramo z ▫$w(e):=\sum_{P_{a,b \ni e}} \frac{1}{n(a,b)}$▫ in ▫$w^\ast (e):=\sum_{P^\ast_{a,b \ni e}} \frac{1}{n^\ast(a,b)}$▫. Določene so porazdelitve uteži ▫$w$▫ in ▫$w^\ast$▫ za nekatere družine grafov.
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