Results 11 to 20 of about 832,958 (281)

Geodesic Distance in Planar Graphs [PDF]

Nuclear Physics B, 2003
We derive the exact generating function for planar maps (genus zero fatgraphs) with vertices of arbitrary even valence and with two marked points at a fixed geodesic distance. This is done in a purely combinatorial way based on a bijection with decorated
Ambjørn, Ambjørn, Bousquet-Mélou, Bousquet-Mélou, Bouttier, Bouttier, Bouttier, Brézin, Chassaing, David, Delmas, Di Francesco, Di Francesco, Distler, E. Guitter, Eynard, Gelfand, J. Bouttier, Jimbo, Kawai, Kawamoto, Knizhnik, P. Di Francesco, Schaeffer, Staudacher, Tutte, Tutte, Tutte, Tutte   +28 more
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Signed distance in signed graphs [PDF]

Linear Algebra and its Applications, 2021
Signed graphs have their edges labeled either as positive or negative. Here we introduce two types of signed distance matrix for signed graphs. We characterize balance in signed graphs using these matrices and we obtain explicit formulae for the distance spectrum of some unbalanced signed graphs.
Shahul K. Hameed, T.V. Shijin, P. Soorya, K.A. Germina, Thomas Zaslavsky   +4 more
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Monophonic Distance in Graphs [PDF]

Discrete Mathematics, Algorithms and Applications, 2011
For any two vertices u and v in a connected graph G, a u – v path is a monophonic path if it contains no chords, and the monophonic distance dm(u, v) from u to v is defined as the length of a longest u – v monophonic path in G. A u – v monophonic path of length dm(u, v) is called a u – v monophonic. The monophonic eccentricity em(v) of a vertex v in G
Titus, P., Santhakumaran, A.P.
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Distance in stratified graphs [PDF]

Czechoslovak Mathematical Journal, 2000
A stratified graph is an ordered pair \((G,S)\), where \(G\) is an undirected graph and \(S\) is a partition of its vertex set \(V(G)\) into classes called strata. For any stratum \(X\) the concepts analogous to the basic concepts concerning distance may be defined, namely \(X\)-eccentricity, \(X\)-radius, \(X\)-diameter, \(X\)-center, \(X\)-periphery.
Chartrand, Gary, Hansen, Lisa, Rashidi, Reza, Sherwani, Naveed   +3 more
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Distance labeling in graphs [PDF]

Journal of Algorithms, 2004
Summary: We consider the problem of labeling the nodes of a graph in a way that will allow one to compute the distance between any two nodes directly from their labels (without using any additional information). Our main interest is in the minimal length of labels needed in different cases.
Gavoille, Cyril, Peleg, David, Pérennes, Stéphane, Raz, Ran   +3 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 ...
Hansberg, Adriana, Meierling, Dirk, Volkmann, Lutz   +2 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, V A. Rasila, Ambat Vijayakumar   +2 more
doaj   +1 more source

Geometric aspects of 2-walk-regular graphs [PDF]

, 2013
A $t$-walk-regular graph is a graph for which the number of walks of given length between two vertices depends only on the distance between these two vertices, as long as this distance is at most $t$. Such graphs generalize distance-regular graphs and $t$
Cámara, Marc, Koolen, Jack H., Park, Jongyook, van Dam, Edwin R.   +3 more
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Distinct Distances in Graph Drawings [PDF]

The Electronic Journal of Combinatorics, 2008
The distance-number of a graph $G$ is the minimum number of distinct edge-lengths over all straight-line drawings of $G$ in the plane. This definition generalises many well-known concepts in combinatorial geometry. We consider the distance-number of trees, graphs with no $K^-_4$-minor, complete bipartite graphs, complete graphs, and cartesian products.
Carmi, Paz, Dujmovic, Vida, Morin, Pat, Wood, David R.   +3 more
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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, Tayna Lobo, Renata Del-Vecchio   +2 more
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