Characterizing the interval function of a connected graph
نویسندگان
چکیده
منابع مشابه
The Interval Function of a Connected Graph and a Characterization of Geodetic Graphs
The interval function (in the sense of H.M.Mulder) is an important tool for studying those properties of a connected graph that depend on the distance between vertices. An axiomatic characterization of the interval function of a connected graph was published by Nebeský in 1994. In Section 2 of the present paper, a simpler and shorter proof of that characterization will be given. In Section 3, a...
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a dominating set $d subseteq v$ of a graph $g = (v,e)$ is said to be a connected cototal dominating set if $langle d rangle$ is connected and $langle v-d rangle neq phi$, contains no isolated vertices. a connected cototal dominating set is said to be minimal if no proper subset of $d$ is connected cototal dominating set. the connected cototal domination number $gamma_{ccl}(g)$ of $g$ is the min...
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A fundamental notion in metric graph theory is that of the interval function I : V × V → 2V − {∅} of a (finite) connected graph G = (V,E), where I(u, v) = { w | d(u, w) + d(w, v) = d(u, v) } is the interval between u and v. An obvious question is whether I can be characterized in a nice way amongst all functions F : V × V → 2V − {∅}. This was done in [13, 14, 16] by axioms in terms of propertie...
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ژورنال
عنوان ژورنال: Mathematica Bohemica
سال: 1998
ISSN: 0862-7959,2464-7136
DOI: 10.21136/mb.1998.126307