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The Threshold Dimension and Irreducible Graphs
Discussiones Mathematicae Graph Theory, 2023 Let G be a graph, and let u, v, and w be vertices of G. If the distance between u and w does not equal the distance between v and w, then w is said to resolve u and v.
Mol Lucas +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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Weiner Polynomials to Generalize the Distance of Some Composite Graphs from Special Graphs [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2008 It is not easy to find the Wiener polynomials for generalized distance of compound graphs constructed in the form and for any two disjoint connected graphs and .Therefore, in this paper, we obtain Wiener polynomials for generalized distance of and ...
Ali Ali, Ahmed Ali
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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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Geodesic distance in planar graphs [PDF]
Nuclear Physics B, 2003 38 pages, 8 figures, tex, harvmac ...
Bouttier, Jérémie +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 +2 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 +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 +2 more
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High Girth Column-Weight-Two LDPC Codes Based on Distance Graphs
EURASIP Journal on Wireless Communications and Networking, 2007 LDPC codes of column weight of two are constructed from minimal distance graphs or cages. Distance graphs are used to represent LDPC code matrices such that graph vertices that represent rows and edges are columns. The conversion of a distance graph into
Gabofetswe Malema, Michael Liebelt
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Weiner Polynomials for Generalization of Distance for Some Special Graphs [PDF]
Al-Rafidain Journal of Computer Sciences and Mathematics, 2006 The minimum distance of a vertex v to an set of vertices of a graph G is defined as : . The n-Wiener polynomial for this distance of a graph G is defined as , where is the number of order pairs (v,S), , such that , and is the diameter
Ali Ali, Ahmed Ali
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