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- W1988302811 abstract "For a nontrivial connected graph G of order n and a linear ordering s: v 1, v 2, …, v n of vertices of G, define $$ d(s) = sumlimits_{i = 1}^{n - 1} {d(v_i ,v_{i + 1} )} $$ . The traceable number t(G) of a graph G is t(G) = min{d(s)} and the upper traceable number t +(G) of G is t +(G) = max{d(s)}, where the minimum and maximum are taken over all linear orderings s of vertices of G. We study upper traceable numbers of several classes of graphs and the relationship between the traceable number and upper traceable number of a graph. All connected graphs G for which t +(G) − t(G) = 1 are characterized and a formula for the upper traceable number of a tree is established." @default.
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- W1988302811 date "2008-03-01" @default.
- W1988302811 modified "2023-10-10" @default.
- W1988302811 title "The upper traceable number of a graph" @default.
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- W1988302811 doi "https://doi.org/10.1007/s10587-008-0016-9" @default.
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