A study on prime arithmetic integer additive set-indexers of graphs
نویسنده
چکیده
Let N0 be the set of all non-negative integers and P(N0) be its power set. An integer additive set-indexer (IASI) is defined as an injective function f : V (G) → P(N0) such that the induced function f : E(G)→ P(N0) defined by f(uv) = f(u)+f(v) is also injective, where N0 is the set of all non-negative integers. A graph G which admits an IASI is called an IASI graph. An IASI of a graph G is said to be an arithmetic IASI if the elements of the set-labels of all vertices and edges of G are in arithmetic progressions. In this paper, we discuss about a particular type of arithmetic IASI called prime arithmetic IASI.
منابع مشابه
Weak Integer Additive Set-Indexers of Certain Graph Products
An integer additive set-indexer is defined as an injective function f : V (G) → 2N0 such that the induced function gf : E(G) → 2N0 defined by gf (uv) = f(u) + f(v) is also injective, where f(u) + f(v) is the sumset of f(u) and f(v). If gf (uv) = k ∀ uv ∈ E(G), then f is said to be a k-uniform integer additive set-indexers. An integer additive set-indexer f is said to be a weak integer additive ...
متن کاملA Study on the Nourishing Number of Graphs and Graph Powers
Let N0 be the set of all non-negative integers and P(N0) be its power set. Then, an integer additive set-indexer (IASI) of a given graph G is defined as an injective function f : V (G) → P(N0) such that the induced edge-function f : E(G) → P(N0) defined by f(uv) = f(u) + f(v) is also injective, where f(u) + f(v) is the sumset of f(u) and f(v). An IASI f of G is said to be a strong IASI of G if ...
متن کاملThe second geometric-arithmetic index for trees and unicyclic graphs
Let $G$ be a finite and simple graph with edge set $E(G)$. The second geometric-arithmetic index is defined as $GA_2(G)=sum_{uvin E(G)}frac{2sqrt{n_un_v}}{n_u+n_v}$, where $n_u$ denotes the number of vertices in $G$ lying closer to $u$ than to $v$. In this paper we find a sharp upper bound for $GA_2(T)$, where $T$ is tree, in terms of the order and maximum degree o...
متن کاملUnique Prime Cartesian Factorization of Graphs over Finite Fields
A fundamental result, due to Sabidussi and Vizing, states that every connected graph has a unique prime factorization relative to the Cartesian product; but disconnected graphs are not uniquely prime factorable. This paper describes a system of modular arithmetic on graphs under which both connected and disconnected graphs have unique prime Cartesian factorizations.
متن کاملThe automorphism group of the reduced complete-empty $X-$join of graphs
Suppose $X$ is a simple graph. The $X-$join $Gamma$ of a set ofcomplete or empty graphs ${X_x }_{x in V(X)}$ is a simple graph with the following vertex and edge sets:begin{eqnarray*}V(Gamma) &=& {(x,y) | x in V(X) & y inV(X_x) },\ E(Gamma) &=& {(x,y)(x^prime,y^prime) | xx^prime in E(X) or else x = x^prime & yy^prime in E(X_x)}.end{eqnarray*}The $X-$join graph $Gamma$ is said to be re...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2017