On R degrees of vertices and R indices of graphs
نویسنده
چکیده
Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: R degree. And also we define R indices of a simple connected graph by using the R degree concept. We compute the R indices for well-known simple connected graphs such as paths, stars, complete graphs and cycles.
منابع مشابه
Note on multiple Zagreb indices
The Zagreb indices are the oldest graph invariants used in mathematical chemistry to predict the chemical phenomena. In this paper we define the multiple versions of Zagreb indices based on degrees of vertices in a given graph and then we compute the first and second extremal graphs for them.
متن کاملA study on some properties of leap graphs
In a graph G, the first and second degrees of a vertex v is equal to thenumber of their first and second neighbors and are denoted by d(v/G) andd 2 (v/G), respectively. The first, second and third leap Zagreb indices are thesum of squares of second degrees of vertices of G, the sum of products of second degrees of pairs of adjacent vertices in G and the sum of products of firs...
متن کاملOn leap Zagreb indices of graphs
The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.
متن کاملCalculating Different Topological Indices of Von Neumann Regular Graph of Z_(p^α )
By the Von Neumann regular graph of R, we mean the graph that its vertices are all elements of R such that there is an edge between vertices x,y if and only if x+y is a von Neumann regular element of R, denoted by G_Vnr (R). For a commutative ring R with unity, x in R is called Von Neumann regular if there exists x in R such that a=a2 x. We denote the set of Von Neumann regular elements by V nr...
متن کاملOn zero-divisor graphs of quotient rings and complemented zero-divisor graphs
For an arbitrary ring $R$, the zero-divisor graph of $R$, denoted by $Gamma (R)$, is an undirected simple graph that its vertices are all nonzero zero-divisors of $R$ in which any two vertices $x$ and $y$ are adjacent if and only if either $xy=0$ or $yx=0$. It is well-known that for any commutative ring $R$, $Gamma (R) cong Gamma (T(R))$ where $T(R)$ is the (total) quotient ring of $R$. In this...
متن کاملDirected domination in oriented hypergraphs
ErdH{o}s [On Sch"utte problem, Math. Gaz. 47 (1963)] proved that every tournament on $n$ vertices has a directed dominating set of at most $log (n+1)$ vertices, where $log$ is the logarithm to base $2$. He also showed that there is a tournament on $n$ vertices with no directed domination set of cardinality less than $log n - 2 log log n + 1$. This notion of directed domination number has been g...
متن کامل