Maximum Degree Growth of the Iterated Line Graph
نویسندگان
چکیده
منابع مشابه
Maximum Degree Growth of the Iterated Line Graph
Let ∆k denote the maximum degree of the k th iterated line graph L(G). For any connected graph G that is not a path, the inequality ∆k+1 ≤ 2∆k − 2 holds. Niepel, Knor, and Šoltés [3] have conjectured that there exists an integer K such that, for all k ≥ K, equality holds; that is, the maximum degree ∆k attains the greatest possible growth. We prove this conjecture using induced subgraphs of max...
متن کاملMinimum Degree Growth of the Iterated Line Graph
Let δk denote the minimum degree of the k th iterated line graph L(G). For any connected graph G that is not a path, the inequality δk+1 ≥ 2δk − 2 holds. Niepel, Knor, and Šoltés [5] have conjectured that there exists an integer K such that, for all k ≥ K, equality holds; that is, the minimum degree δk attains the least possible growth. We prove this conjecture by extending the methods we used ...
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ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 1999
ISSN: 1077-8926
DOI: 10.37236/1460