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Powers of chordal graphs

  • R. Balakrishnan (a1) and P. Paulraja (a1)

Abstract

An undirected simple graph G is called chordal if every circle of G of length greater than 3 has a chord. For a chordal graph G, we prove the following: (i) If m is an odd positive integer, Gm is chordal. (ii) If m is an even positive integer and if Gm is not chordal, then none of the edges of any chordless cycle of Gm is an edge of Gr, r < m.

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References

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[1]Balakrishnan, R. and Paulraja, P., ‘Graphs whose squares are chordal,’ Indian J. Pure Appl. Math. 12 (1981), 193194 with erratum, same J. 12 (1981), 1062.
[2]Bondy, J. A. and Murty, U. S. R., Graph theory with applications (Macmillan 1976).
[3]Laskar, Renu and Shier, D., ‘On chordal graphs,’ Congressus Numerantium, 29 (1980), 579588.
[4]Laskar, Renu and Shier, D., On powers and centres of chordal graphs, Technical Report # 357 (Department of Mathematical Sciences, Clemson University, South Carolina, 02 1981).
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