Minimal induced subgraphs of two classes of 2-connected non-Hamiltonian graphs

Hamiltonian Connected Graphs Involving Forbidden Subgraphs

We consider the pair of graphs S and T such that every 3-connected {S, T}-free graph is hamiltonian connected. Such pairs are called hamiltonian connected pairs. We show three new hamiltonian connected pairs. Combing our results and a result of Shepherd, we conclude that if {S, T} is a pair of graphs such that every 2-connected {S, T}-free graph is hamiltonian then every 3-connected {S, T}-free...

On Finding Minimal Two-Connected Subgraphs

Wepresent e cient parallel algorithms for the problems of nding a minimal2-edge-connected spanning subgraph of a 2-edge-connected graph and nding a minimalbiconnected spanning subgraph of a biconnected graph. The parallel algorithms run in polylog time using a linear number of PRAM processors. We also give linear time sequential algorithms for minimally augmenting a spanning tree into a 2-edge-...

Spanning 2-Connected Subgraphs in Alphabet Graphs, Special Classes of Grid Graphs

Two New Classes of Hamiltonian Graphs

We prove that a triangular grid without local cuts is (almost) always Hamiltonian. This suggests an efficient scheme for rendering triangulated manifolds by graphics hardware. We also show that the Hamiltonian Cycle problem is NP-Complete for planar subcubic graphs of arbitrarily high girth. As a by-product we prove that there exist tri-Hamiltonian planar subcubic graphs of arbitrarily high gir...

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...