Now showing items 1-6 of 6
| Abstract: | Almost self-centered graphs were recently introduced as the graphs with exactly two non-central vertices. In this paper we characterize almost selfcentered graphs among median graphs and among chordal graphs. In the first case P4 and the graphs obtained from hypercubes by attaching to them a single leaf are the only such graphs. Among chordal graph the variety of almost self-centered graph is much richer, despite the fact that their diameter is at most 3. We also discuss almost self-centered graphs among partial cubes and among k-chordal graphs, classes of graphs that generalize median and chordal graphs, respectively. Characterizations of almost self-centered graphs among these two classes seem elusive |
| Description: | TAIWANESE JOURNAL OF MATHEMATICS Vol. 16, No. 5, pp. 1911-1922, October 2012 |
| URI: | http://dyuthi.cusat.ac.in/purl/4213 |
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| Almost Self-Centered Median And Chordal Graphs.pdf | (225.6Kb) |
| Abstract: | Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2 dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced. |
| Description: | Discrete Optimization 12 (2014) 150–154 |
| URI: | http://dyuthi.cusat.ac.in/purl/4220 |
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| Equal opportuni ... raphs, and Wiener game.pdf | (367.3Kb) |
| Abstract: | The median of a profile = (u1, . . . , uk ) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of . It is shown that for profiles with diameter the median set can be computed within an isometric subgraph of G that contains a vertex x of and the r -ball around x, where r > 2 − 1 − 2 /| |. The median index of a graph and r -joins of graphs are introduced and it is shown that r -joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles. |
| Description: | Discrete Applied Mathematics 156 (2008) 2882–2889 |
| URI: | http://dyuthi.cusat.ac.in/purl/4216 |
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| The median func ... with bounded profiles.pdf | (410.2Kb) |
| Abstract: | A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed |
| Description: | University of Ljubljana Institute of Mathematics, Physics and Mechanics Department of Mathematics Preprint series, Vol. 46 (2008), 1046 |
| URI: | http://dyuthi.cusat.ac.in/purl/4237 |
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| Median Graphs, ... nd Geodetic Number Two.pdf | (256.4Kb) |
| Abstract: | The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered. |
| URI: | http://dyuthi.cusat.ac.in/purl/4217 |
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| On the generali ... blemantimedian subsets.pdf | (142.4Kb) |
| Abstract: | A profile on a graph G is any nonempty multiset whose elements are vertices from G. The corresponding remoteness function associates to each vertex x 2 V.G/ the sum of distances from x to the vertices in the profile. Starting from some nice and useful properties of the remoteness function in hypercubes, the remoteness function is studied in arbitrary median graphs with respect to their isometric embeddings in hypercubes. In particular, a relation between the vertices in a median graph G whose remoteness function is maximum (antimedian set of G) with the antimedian set of the host hypercube is found. While for odd profiles the antimedian set is an independent set that lies in the strict boundary of a median graph, there exist median graphs in which special even profiles yield a constant remoteness function. We characterize such median graphs in two ways: as the graphs whose periphery transversal number is 2, and as the graphs with the geodetic number equal to 2. Finally, we present an algorithm that, given a graph G on n vertices and m edges, decides in O.mlog n/ time whether G is a median graph with geodetic number 2 |
| Description: | Discrete Applied Mathematics 157 (2009) 3679- 3688 |
| URI: | http://dyuthi.cusat.ac.in/purl/4197 |
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| On the remoteness function in median graphs.pdf | (609.5Kb) |
Now showing items 1-6 of 6
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