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A characterization of strongly chordal graphs

✍ Scribed by Elias Dahlhaus; Paul D. Manuel; Mirka Miller

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
119 KB
Volume
187
Category
Article
ISSN
0012-365X

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✦ Synopsis

In this paper, we present a simple charactrization of strongly chordal graphs. A chordal graph is strongly chordal if and only if every cycle on six or more vertices has an induced triangle with exactly two edges of the triangle as the chords of the cycle. (~

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Chordal graphs are graphs with the property that each cycle of length greater than 3 has two non-consecutive vertices that are joined by an edge. An important subclass of chordal graphs are strongly chordal graphs (Farber, 1983). Chordal graphs appear for example in the design of acyclic data base s

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## Abstract Suppose __G = (V, E)__ is a graph in which every vertex __x__ has a non‐negative real number __w(x)__ as its weight. The __w__‐distance sum of a vertex __y__ is __D~G, w~(y)__ = Οƒ~xβ‰…v~ __d(y, x)w(x).__ The __w__‐median of __G__ is the set of all vertices __y__ with minimum __w__‐distanc