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- W2166121119 abstract "For a connected graph Gof order n >2 and a linear ordering s: v1, v2, . . . , vn of vertices of G, d(s) = n−1 P i=1 d(vi, vi+1), where d(vi, vi+1) is the distance between vi and vi+1. The upper traceable number t + (G) of Gis t + (G)=max{d(s)}, where the maximum is taken over all linear orderings sof vertices of G. It is known that if T is a tree of order n >3,then2n−3 6 t + (T) 6 ⌊n 2 /2⌋−1and t + (T) 6 ⌊n 2 /2⌋−3if T 6 Pn. Allpairs n, kfor which thereexists a tree T of order nand t + (T)= kare determinedanda characterization of all those trees of order n > 4 with upper traceable number ⌊n 2 /2⌋ −3 is established. For a connected graph G of order n > 3, it is known that n −1 6 t + (G) 6 ⌊n 2 /2⌋ −1. We investigate the problem of determining possible pairs n, k of positive integers that are realizable as the order and upper traceable number of some connected graph." @default.
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- W2166121119 date "2008-01-01" @default.
- W2166121119 modified "2023-09-23" @default.
- W2166121119 title "On upper traceable numbers of graphs" @default.
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- W2166121119 doi "https://doi.org/10.21136/mb.2008.140628" @default.
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