Order and radius of (2k−1)-connected graphs

Tatsuya Iida; Kurato Kobayashi

doi:10.55937/sut/1173205983

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Home > Journals > SUT J. Math. > Volume 42 > Issue 2 > Article

June 2006 Order and radius of

(2k - 1)

-connected graphs

Tatsuya Iida, Kurato Kobayashi

Author Affiliations +

Tatsuya Iida,¹ Kurato Kobayashi²
¹Department of Mathematical Information Science, Tokyo University of Science 1-3 Kagurazaka, Shinjuku-ku, Tokyo, 162-8601, Japan
²Hitachi Software Engineering Co., Ltd. 4-12-7 Higashishinagawa, Shinagawa-ku, Tokyo, 140-0002, Japan

SUT J. Math. 42(2): 335-356 (June 2006). DOI: 10.55937/sut/1173205983

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Abstract

We show that if $k$ is an integer with $k \ge 3$ and $G$ is a $(2k - 1)$ -connected graph with radius $r$ , then $\left| {V(G)} \right| \ge 2kr - 2k - 2$ .

Acknowledgement

The authors would like to thank Professor Yoshimi Egawa for his valuable advice and encouragement.

Citation

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Tatsuya Iida. Kurato Kobayashi. "Order and radius of $(2k - 1)$ -connected graphs." SUT J. Math. 42 (2) 335 - 356, June 2006. https://doi.org/10.55937/sut/1173205983