منابع مشابه
on wiener index of graph complements
let $g$ be an $(n,m)$-graph. we say that $g$ has property $(ast)$if for every pair of its adjacent vertices $x$ and $y$, thereexists a vertex $z$, such that $z$ is not adjacentto either $x$ or $y$. if the graph $g$ has property $(ast)$, thenits complement $overline g$ is connected, has diameter 2, and itswiener index is equal to $binom{n}{2}+m$, i.e., the wiener indexis insensitive of any other...
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Orthogonal representations are used to show that complements of certain sparse graphs have (positive semidefinite) minimum rank at most 4. This bound applies to the complement of a 2-tree and to the complement of a unicyclic graph. Hence for such graphs, the sum of the minimum rank of the graph and the minimum rank of its complement is at most two more than the order of the graph. The minimum r...
متن کاملOn Wiener Index of Graph Complements
Let G be an (n, m)-graph. We say that G has property (∗) if for every pair of its adjacent vertices x and y, there exists a vertex z, such that z is not adjacent to either x or y. If the graph G has property (∗), then its complement G is connected, has diameter 2, and its Wiener index is equal to ( n 2 ) + m, i.e., the Wiener index is insensitive of any other structural details of the graph G. ...
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For any g > 2 we construct a graph Γg ⊂ S whose exteriorMg = S\N(Γg) supports a complete finite-volume hyperbolic structure with one toric cusp and a connected geodesic boundary of genus g. We compute the canonical decomposition and the isometry group of Mg, showing in particular that any selfhomeomorphism of Mg extends to a self-homeomorphism of the pair (S ,Γg), and that Γg is chiral. Buildin...
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GP 2 is a non-deterministic programming language for computing by graph transformation. One of the design goals for GP 2 is syntactic and semantic simplicity, to facilitate formal reasoning about programs. In this paper, we demonstrate with four case studies how programmers can prove termination and partial correctness of their solutions. We argue that GP 2’s graph transformation rules, togethe...
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ژورنال
عنوان ژورنال: Formalized Mathematics
سال: 2020
ISSN: 1898-9934,1426-2630
DOI: 10.2478/forma-2020-0004