Elementary proofs of (relatively) recent characterizations of Eulerian graphs

The irregularity and total irregularity of Eulerian graphs

For a graph G, the irregularity and total irregularity of G are defined as irr(G)=∑_(uv∈E(G))〖|d_G (u)-d_G (v)|〗 and irr_t (G)=1/2 ∑_(u,v∈V(G))〖|d_G (u)-d_G (v)|〗, respectively, where d_G (u) is the degree of vertex u. In this paper, we characterize all ‎connected Eulerian graphs with the second minimum irregularity, the second and third minimum total irregularity value, respectively.

the effects of integrating cooperative learning into vocabulary learning of elementary school students

the purpose of the research is to examine if integrating cooperative learning into vocabulary learning helps to increase word recognition of students in an elementary school in iran. it tries to investigate whether cooperative learning approach enables students to improve their language learning. this research used stad (students team achievement division) as a cooperative model in this study. ...

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...

Proofs in Elementary Analysis

Quillen’s Elementary Proofs

Recall 1.1. The construction of the Steenrod squares and powers proceeds in the following steps 1. For a space X, the p-th cartesian power Xp is acted on cyclically by Z/p and it fits into a fibration Xp → EZ/p×Z/p Xp → BZ/p 2. If x ∈ H∗(X, Z/p), one defines u × · · · × u ∈ H∗(Xp, Z/p) and extends this class to ũ ∈ H(EZ/p×Z/p Xp; Z/p) by a construction on the chain level. 3. ũ is then pulled ba...