Results 11 to 20 of about 177,806 (308)
On the editing distance of graphs [PDF]
Journal of Graph Theory, 2008 AbstractAn edge‐operation on a graph G is defined to be either the deletion of an existing edge or the addition of a nonexisting edge. Given a family of graphs $\cal G$, the editing distance from G to $\cal G$ is the smallest number of edge‐operations needed to modify G into a graph from $\cal G$.
Maria Axenovich +2 more
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AKCE International Journal of Graphs and Combinatorics, 2020 The status of a vertex , denoted by , is the sum of the distances between and all other vertices in a graph . The first and second status connectivity indices of a graph are defined as and respectively, where denotes the edge set of .
Harishchandra S. Ramane +2 more
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Distance Domination and Distance Irredundance in Graphs [PDF]
The Electronic Journal of Combinatorics, 2007 A set $D\subseteq V$ of vertices is said to be a (connected) distance $k$-dominating set of $G$ if the distance between each vertex $u\in V-D$ and $D$ is at most $k$ (and $D$ induces a connected graph in $G$). The minimum cardinality of a (connected) distance $k$-dominating set in $G$ is the (connected) distance $k$-domination number of $G$, denoted ...
Adriana Hansberg +2 more
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Dualizing Distance-Hereditary Graphs
Discussiones Mathematicae Graph Theory, 2021 Distance-hereditary graphs can be characterized by every cycle of length at least 5 having crossing chords. This makes distance-hereditary graphs susceptible to dualizing, using the common extension of geometric face/vertex planar graph duality to cycle ...
McKee Terry A.
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Exact Distance Graphs of Product Graphs [PDF]
Graphs and Combinatorics, 2019 Given a graph $G$, the exact distance-$p$ graph $G^{[\natural p]}$ has $V(G)$ as its vertex set, and two vertices are adjacent whenever the distance between them in $G$ equals $p$. We present formulas describing the structure of exact distance-$p$ graphs of the Cartesian, the strong, and the lexicographic product.
Brešar, Boštjan +3 more
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Steiner Wiener index of block graphs
AKCE International Journal of Graphs and Combinatorics, 2020 Let S be a set of vertices of a connected graph G. The Steiner distance of S is the minimum size of a connected subgraph of G containing all the vertices of S.
Matjaž Kovše +2 more
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On the graph of large distances [PDF]
Discrete & Computational Geometry, 1989 Let \(S\) be a set of \(n\) points in the plane and let \(d_1>d_2>..\). be the different distances determined by the set \(S\). The graph \(G(S,k)\) is considered whose vertex set is S and in which two vertices are adjacent if and only if their distance is at least \(k\). The chromatic number \(\chi(G(S,k))\) of \(G(S,k)\) is studied. It is proved that
Erdös, P. +2 more
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Open Distance-Pattern Uniform Graphs [PDF]
, 2009 All graphs considered in this paper are finite, simple, undirected and connected. For graph theoretic terminology we refer to Harary [6].
Jose, Bibin K.
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On the distance spectrum of certain distance biregular graphs
The American Journal of Combinatorics, 2023 In this article we present an infinite family of bipartite distance biregular graphs having an arbitrarily large diameter and whose distance matrices have exactly four distinct eigenvalues. This result answers a question posed by F.
Miriam Abdon +2 more
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Distance-unbalancedness of graphs [PDF]
Applied Mathematics and Computation, 2021 14 pages, 3 ...
Miklavič, Štefko, Šparl, Primož
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