‎‎let r be a non-commutative ring with unity‎. ‎the commuting graph‎ ‎of $r$ denoted by $gamma(r)$‎, ‎is a graph with a vertex set‎ ‎$rsetminus z(r)$ and two vertices $a$ and $b$ are adjacent if and only if‎ ‎$ab=ba$‎. ‎in this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. it is shown that‎, ‎$gamma(r)$ is the disjoint ...

The serological and physicochemical properties of the following three forms of human anti-gamma-globulin factors were compared: (a) rheumatoid factors; (b) Milgrom type anti-gamma-globulin factors; and (c) factors directed against an antigen in human gammaG-globulin that is hidden in the intact molecule and revealed by enzymatic digestion at low pH. The property common to these factors is abili...

Let ( L , Γ ) $(\mathfrak {L},\Gamma )$ be an isometric boundary pair associated with a closed symmetric linear relation T in Krein space H $\mathfrak {H}$ . M $M_\Gamma$ the Weyl family corresponding to We cope two main topics. First, since need not (generalized) Nevanlinna, characterization of closure and adjoint z $M_\Gamma (z)$ for some ∈ C ∖ R $z\in \mathbb {C}\setminus {R}$ becomes nontri...

‎‎Let $R$ be a non-commutative ring with unity‎. ‎The commuting graph‎ of $R$ denoted by $Gamma(R)$‎, ‎is a graph with a vertex set‎ ‎$Rsetminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if‎ $ab=ba$‎. ‎In this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. It is shown that‎, ‎$Gamma(R)$ is the disjoint ...

In a non-complete graph $Gamma$, a vertex triple $(u,v,w)$ with $v$ adjacent to both $u$ and $w$ is called a $2$-geodesic if $uneq w$ and $u,w$ are not adjacent. The graph $Gamma$ is said to be   $2$-geodesic transitive if its automorphism group is transitive on arcs, and also on 2-geodesics. We first produce a reduction theorem for the family of $2$-geodesic transitive graphs of prime power or...