منابع مشابه
Hamiltonian Connected Line Graphs
Thomassen conjectured [8] that every 4-connected line graph is hamiltonian. An hourglass is a graph isomorphic to K5−E(C), where C is a cycle of length 4 in K5. In [2], it is shown that every 4-connected line graph without an induced subgraph isomorphic to the hourglass is hamiltonian connected. In this note, we prove that every 3-connected, essentially 4-connected hourglass-free line graph is ...
متن کاملPlanarity of iterated line graphs
The line index of a graph G is the smallest k such that the kth iterated line graph of G is nonplanar. We show that the line index of a graph is either infinite or it is at most 4. Moreover, we give a full characterization of all graphs with respect to their line index. © 2007 Elsevier B.V. All rights reserved.
متن کاملConnectivity of iterated line graphs
Let k ≥ 0 be an integer and L(G) be k-th iterated line graph. Niepel, Knor, and Šolteś proved that if G is a 4-connected graph, then κ(L(G)) ≥ 4δ(G) − 6. We prove that the connectivity of G can be relaxed. It is proved that if G is an essentially 4-edge-connected and 3-connected graph, then κ(L(G)) ≥ 4δ(G) − 6. Similar bounds are obtained for essentially 4-edge-connected and 2-connected (1-conn...
متن کاملD-Spectrum and D-Energy of Complements of Iterated Line Graphs of Regular Graphs
The D-eigenvalues {µ1,…,µp} of a graph G are the eigenvalues of its distance matrix D and form its D-spectrum. The D-energy, ED(G) of G is given by ED (G) =∑i=1p |µi|. Two non cospectral graphs with respect to D are said to be D-equi energetic if they have the same D-energy. In this paper we show that if G is an r-regular graph on p vertices with 2r ≤ p - 1, then the complements of iterated lin...
متن کاملPancyclicity of hamiltonian line graphs
Let f(n) be the smallest integer such that for every graph G of order n with minimum degree 3(G)>f(n), the line graph L(G) of G is pancyclic whenever L(G) is hamiltonian. Results are proved showing that f(n) = ®(n 1/3).
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2002
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00442-3