A sufficient condition for pancyclic graphs

New sufficient conditions for Hamiltonian paths

“…To the best of our knowledge, the latest and the best (so far) result of "Rahman-Kaykobad" condition was reported in [9]. In particular, in [9], the authors show that "Rahman-Kaykobad" condition is "almost" sufficient to make a graph pancyclic, where a graph is pancyclic if it contains a cycle of length for 3 ≤ ≤ .…”

“…Theorem 7 (see [9]). Let be a 2-connected graph of order ≥ 6, which satisfies the "Rahman-Kaykobad" condition.…”

Some Sufficient Conditions on Pancyclic Graphs

“…The equation (2.2) is called signless Laplacian eigen-equation of G. Lemma 2.1 [12] Let G be a graph of order n with degree sequence d1 [11] Let G be a connected graph of order n with m deges. Then…”

New Sufficient Conditions for Hamiltonian Paths

“…The sufficient conditions of Theorems 4 , 5 , and 6 can be seen as incremental improvements over the result of Rahman and Kaykobad [ 5 ]. To the best of our knowledge, the latest and the best (so far) result of “Rahman-Kaykobad” condition was reported in [ 9 ]. In particular, in [ 9 ], the authors show that “Rahman-Kaykobad” condition is “almost” sufficient to make a graph pancyclic, where a graph is pancyclic if it contains a cycle of length k for 3 ≤ k ≤ n .…”