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Pancyclic and panconnected line graphs
Author(s) -
Benhocine Abdelhamid,
Fouquet JeanLuc
Publication year - 1987
Publication title -
journal of graph theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 54
eISSN - 1097-0118
pISSN - 0364-9024
DOI - 10.1002/jgt.3190110313
Subject(s) - combinatorics , mathematics , graph , degree (music) , bound graph , discrete mathematics , pancyclic graph , line graph , graph power , 1 planar graph , physics , acoustics
Let G be a graph of order n ⩾ 3. We prove that if G is k ‐connected ( k ⩾ 2) and the degree sum of k + 1 mutually independent vertices of G is greater than 1/3( k + 1)( n + 1), then the line graph L(G) of G is pancyclic. We also prove that if G is such that the degree sum of every 2 adjacent vertices is at least n , then L(G) is panconnected with some exceptions.
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