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| 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: | A graph G is strongly distance-balanced if for every edge uv of G and every i 0 the number of vertices x with d.x; u/ D d.x; v/ 1 D i equals the number of vertices y with d.y; v/ D d.y; u/ 1 D i. It is proved that the strong product of graphs is strongly distance-balanced if and only if both factors are strongly distance-balanced. It is also proved that connected components of the direct product of two bipartite graphs are strongly distancebalanced if and only if both factors are strongly distance-balanced. Additionally, a new characterization of distance-balanced graphs and an algorithm of time complexity O.mn/ for their recognition, wheremis the number of edges and n the number of vertices of the graph in question, are given |
| Description: | European Journal of Combinatorics 30 (2009) 1048- 1053 |
| URI: | http://dyuthi.cusat.ac.in/purl/4198 |
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| Strongly distan ... phs and graph products.pdf | (373.0Kb) |
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