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Discrete Mathematics, 1992 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Distance independence in graphs
Discussiones Mathematicae Graph Theory, 2011 For a set D of positive integers, we define a vertex set SV (G) to be D-independent if u,v 2 S implies the distance d(u,v) 㘲 D. The D-independence numberD(G) is the maximum cardinality of a D-independent set. In particular, the independence number (G) = {1}(G).
J. Louis Sewell, Peter J. Slater
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Metric Locations in Pseudotrees: A Survey and New Results
MathematicsThis paper presents a comprehensive review of the literature on the original concept of metric location, along with its various adaptations and extensions that have been developed over time.
José Cáceres, Ignacio M. Pelayo
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Spectral recognition of graphs [PDF]
Yugoslav Journal of Operations Research, 2012 At some time, in the childhood of spectral graph theory, it was conjectured that non-isomorphic graphs have different spectra, i.e. that graphs are characterized by their spectra.
Cvetković Dragoš
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Distances in orientations of graphs
Journal of Combinatorial Theory, Series B, 1978 We prove that there is a function h(k) such that every undirected graph G admits an orientation H with the following property: if an edge uv belongs to a cycle of length k in G, then uv or vu belongs to a directed cycle of length at most h(k) in H. Next, we show that every undirected bridgeless graph of radius r admits an orientation of radius at most $
Vasek Chvátal, Carsten Thomassen
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Bounds for minimum feedback vertex sets in distance graphs and circulant graphs [PDF]
Discrete Mathematics & Theoretical Computer Science, 2008 Graphs and ...
Hamamache Kheddouci, Olivier Togni
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Distance equienergetic graphs of diameter 4
Examples and CounterexamplesLet Γ1, Γ2 and Γ3 be graphs with pairwise disjoint vertex sets. The graph Θ(Γ1,Γ2,Γ3) is obtained from the graphs Γ1∘Γ3 (the corona product) and Γ2 by joining each vertices of Γ1 in Γ1∘Γ3 with every vertices in Γ2.
B.J. Manjunatha +2 more
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Annals of Combinatorics, 2008 Distance-balanced graphs are introduced as graphs in which every edge uv has the following property: The number of vertices closer to u than to v is equal to the number of vertices closer to v than to u. Basic properties of these graphs are obtained.
Jerebic, Janja +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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ON DISTANCE-i-GRAPHS OF DISTANCE-REGULAR GRAPHS
Kyushu Journal of Mathematics, 1994 Let \(G\) be a graph. The distance \(i\)-graph of \(G\) is the graph \(G_ i\) defined on the vertex set of \(G\), and \(u\) and \(v\) are adjacent if and only if the distance between \(u\) and \(v\) is \(i\). This paper studies the distance \(i\)-graph of a distance regular graph and its connected component, and obtains a lot of special features of the
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