Abstract
Let k be an integer. A 2-edge connected graph G is said to be goal-minimally k-elongated (k-GME) if for every edge uv ∈ E(G) the inequality d G−uv (x, y) > k holds if and only if {u, v} = {x, y}. In particular, if the integer k is equal to the diameter of graph G, we get the goal-minimally k-diametric (k-GMD) graphs. In this paper we construct some infinite families of GME graphs and explore k-GME and k-GMD properties of cages.
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(Communicated by Anatolij Dvurečenskij)
This research was supported by the Slovak Scientific Grant Agency VEGA No. 1/0406/09.
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Gyürki, Š. Goal-minimally k-elongated graphs. Math. Slovaca 59, 193–200 (2009). https://doi.org/10.2478/s12175-009-0117-4
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DOI: https://doi.org/10.2478/s12175-009-0117-4