This paper shows that if G is a connected graph of order n such that σ2(G)>2(-1) and L(G) is hamiltonian, then, for n≥43, L(G) is pancyclic. Using the result of Veldman[8] this result settles the conjecture of Benhocine, et.al[1]: Let G be a connected almost bridgeless graph of order n such that If n is sufficintly large,L(G) is pancyclic.
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Tel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math Sci, Tel Aviv, IsraelTel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math Sci, Tel Aviv, Israel
Alon, Yahav
Anastos, Michael
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IST Austria, Klosterneurburg, AustriaTel Aviv Univ, Raymond & Beverly Sackler Fac Exact Sci, Sch Math Sci, Tel Aviv, Israel
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L.R.I, UMR 8623, CNRS and Universit Paris-Sud 11, F-91405 Orsay, France
Institute for Interdisciplinary Research, Jianghan UniversityL.R.I, UMR 8623, CNRS and Universit Paris-Sud 11, F-91405 Orsay, France
Hao LI
Jun Qing CAI
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School of Management, Qufu Normal UniversityL.R.I, UMR 8623, CNRS and Universit Paris-Sud 11, F-91405 Orsay, France
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Nankai Univ, Ctr Combinator, LPMC TJKLC, Tianjin 300071, Peoples R ChinaNankai Univ, Ctr Combinator, LPMC TJKLC, Tianjin 300071, Peoples R China
Qu, Ellen X. Y.
Wang, Jianglu
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Shandong Normal Univ, Sch Math Sci, Jinan 250014, Shandong, Peoples R ChinaNankai Univ, Ctr Combinator, LPMC TJKLC, Tianjin 300071, Peoples R China