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KO50001004-00310012-0131.pdf
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Download
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:301.8 KB
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:Jan 29, 2015 |
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| Title |
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Complete connectivity of a graph
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| Creator |
| Name |
竹中, 淑子
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| Kana |
タケナカ, ヨシコ
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| Romanization |
Takenaka, Yoshiko
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| Affiliation |
Dept. of Administration Engineering, Keio University
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| Link |
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Kitagawa, Genshiro
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| Kana |
キタガワ, ゲンシロウ
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| Affiliation |
The Institute of Statistical Mathematics
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慶応義塾大学工学部
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| Kana |
ケイオウ ギジュク ダイガク コウガクブ
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| Romanization |
Keio gijuku daigaku kogakubu
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1978
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Keio engineering reports
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| Volume |
31
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| Issue |
12
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| Year |
1978
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8
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| Start page |
131
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138
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| Abstract |
The object of this paper is to discuss about the connectivity of a graph G=(X, I') in relation to its adjacency matrix A.
Proposition 1 and Theorem 1 of this paper provide necessary and sufficient conditions for a graph G to be strongly and completely connected, respectively. Theorem 2 shows that there is a critical constant n²-2n+2 for the number of the positive power m, to judge whether the graph G is completely connected or not.
Thus this paper gives a direct proof of Theorem 2, which is due to WIELANDT (1950) and later discussed by HOLLADAY and VARGE (1958), PERKINS (1961) and DULMAGE and MENDELSOHN (1964), on the basis of a new lemma giving a definite insight into the structure of a completely connected graph.
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| Departmental Bulletin Paper
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