A characterization of pancyclic complements of line graphs
نویسندگان
چکیده
منابع مشابه
D-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...
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Clark proved that L(G) is hamiltonian if G is a connected graph of order n 2 6 such that deg u + deg v 2 n 1 p(n) for every edge uv of G, where p(n ) = 0 if n is even and p(n) = 1 if n is odd. Here it is shown that the bound n 1 dn) can be decreased to (2n + 1)/3 if every bridge of G is incident with a vertex of degree 1, which is a necessary condition for hamiltonicity of L(G). Moreover, the c...
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Say that a cycle C almost contains a cycle C− if every edge except one of C− is an edge of C. Call a graph G strongly pancyclic if every nontriangular cycle C almost contains another cycle C− and every nonspanning cycle C is almost contained in another cycle C. This is equivalent to requiring, in addition, that the sizes of C− and C differ by one from the size of C. Strongly pancyclic graphs ar...
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We prove the following theorem. Let G be a graph of order n and let W V(G). If |W | 3 and dG(x)+dG( y) n for every pair of non-adjacent vertices x, y # W, then either G contains cycles C , C, ..., C |W | such that C i contains exactly i vertices from W (i=3, 4, ..., |W | ), or |W |=n and G=Kn 2, n 2 , or else |W |=4, G[W]=K2, 2 . This generalizes a result of J. A. Bondy (1971, J. Combin. Theory...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2005
ISSN: 0012-365X
DOI: 10.1016/j.disc.2004.02.024