Proof of conjectures on remoteness and proximity in graphs
نویسندگان
چکیده
منابع مشابه
New bounds on proximity and remoteness in graphs
The average distance of a vertex $v$ of a connected graph $G$is the arithmetic mean of the distances from $v$ to allother vertices of $G$. The proximity $pi(G)$ and the remoteness $rho(G)$of $G$ are defined as the minimum and maximum averagedistance of the vertices of $G$. In this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...
متن کاملnew bounds on proximity and remoteness in graphs
the average distance of a vertex $v$ of a connected graph $g$is the arithmetic mean of the distances from $v$ to allother vertices of $g$. the proximity $pi(g)$ and the remoteness $rho(g)$of $g$ are defined as the minimum and maximum averagedistance of the vertices of $g$. in this paper we investigate the difference between proximity or remoteness and the classical distanceparameters diameter a...
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We characterize 2–dimensional complexes associated canonically with basis graphs of matroids as simply connected triangle-square complexes satisfying some local conditions. This proves a version of a (disproved) conjecture by Stephen Maurer (Conjecture 3 of S. Maurer, Matroid basis graphs I, JCTB 14 (1973), 216–240). We also establish Conjecture 1 from the same paper about the redundancy of the...
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A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x ∈ V (G) the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary median graphs with respect to their isometr...
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The complement of a graph G is denoted by G. χ(G) denotes the chromatic number and ω(G) the clique number of G. The cycles of odd length at least five are called odd holes and the complements of odd holes are called odd anti-holes. A graph G is called perfect if, for each induced subgraph G of G, χ(G) = ω(G). Classical examples of perfect graphs consist of bipartite graphs, chordal graphs and c...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2014
ISSN: 0166-218X
DOI: 10.1016/j.dam.2014.02.011