A large set of non-Hamiltonian graphs

A large set of non-Hamiltonian graphs

commuting and non -commuting graphs of finit groups

فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...

Non-Isomorphic Smallest Maximally Non-Hamiltonian Graphs

A graph G is maximally non-hamiltonian (MNH) if G is not hamiltonian but becomes hamiltonian after adding an arbitrary new edge. Bondy 2] showed that the smallest size (= number of edges) in a MNH graph of order n is at least d 3n 2 e for n 7. The fact that equality may hold there for innnitely many n was suggested by Bollobbs 1]. This was connrmed by Clark, Entringer and Shapiro (see 5, 6]) an...

A family of large set of size nine

 We investigate the existence of some‎ ‎large sets of size nine‎. ‎The large set $LS[9](2,5,29)$ is constructed and‎ ‎existence of the family $LS[9](2,5,27l+j)$ for $lgeq 1, ‎2leq‎ ‎j

Better Approximations of Non-Hamiltonian Graphs

Although there have been a lot of efforts to seek nice characterization of non-Hamiltonian graphs, little progress has been made so far. An important progress was achieved by Chvital [5, 61 who introduced the class of non-l-tough graphs (Nl T) and the class of non-sub-2-factor graphs (NS2F). Both contain only non-Hamiltonian graphs and the conditions for membership can be checked in non-determi...