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On the k-index of graphs

✍ Scribed by Juraj Bosák

Publisher
Elsevier Science
Year
1971
Tongue
English
Weight
540 KB
Volume
1
Category
Article
ISSN
0012-365X

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✦ Synopsis

Almtngt. Gi~ a ter~ph, p~tn every two vt~rticet which me 5t a dhtance tugate¢ than a fixed intelget k t>l) by a new path of lenltth k. Thus a laaph tranlfor:nati~n ts defined. The least number of itaslttior~ of tht, tr;m~l'ofmalion Such that the last it~rJfion does not change the graph. et called the k-m~t of the ol, iRh~a~ ~aph. In the pre,ent paler the graphs ~re c|assif'wd accordtag to theilr t-tadtcet. The re, its age applied in the study of ~,-called tied grapht §1 Throughout this paper, the symbol k denotes a fixed integer greater than I.

ira graph G is given, denote by f;~(G) the graph obtained from G by joining every two vertices whose distance in G is greater than k by a new path constisting of k new edges and containing k-i new inner vertices of degree 2; .it s supposed that the new paths have no common inner vertices.

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