Muhammad Aasi - Academia.edu (original) (raw)
Papers by Muhammad Aasi
A fixing set F of a graph G is a set of those vertices of the graph G which when assigned distinc... more A fixing set F of a graph G is a set of those vertices of the graph G which when assigned distinct labels removes all the automorphisms from the graph except the trivial one. The fixing number of a graph G, denoted by f ix(G), is the smallest cardinality of a fixing set of G. In this paper, we study the fixing number of composition product, G 1 [G 2 ] and corona product, G 1 ⊙ G 2 of two graphs G 1 and G 2 with orders m and n respectively. We show that for a connected graph G 1 and an arbitrary graph G 2 having l ≥ 1 components G 1 2 , G 2 2 , ... G l 2 , mn − 1 ≥ f ix(G 1 [G 2 ]) ≥ m l i=1 f ix(G i 2). For a connected graph G 1 and an arbitrary graph G 2 , which are not asymmetric, we prove that f ix(G 1 ⊙ G 2) = mf ix(G 2). Further, for an arbitrary connected graph G 1 and an arbitrary graph G 2 we show that f ix(G 1 ⊙ G 2) = max{f ix(G 1), mf ix(G 2)}.
Journal of Mathematics, Dec 7, 2021
Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and... more Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and radio labeling. Secrecy of data in data sciences and in information technology is very necessary as well as the accuracy of data transmission and different channel assignments is maintained. It enhances the graph terminologies for the computer programs. In this paper, we will discuss multidistance radio labeling used for channel assignment problems over wireless communication. A radio labeling is a one-to-one mapping ℘: V(G) ⟶ Z + satisfying the condition |℘(μ) − ℘(μ′)| ≥ diam(G) + 1 − d(μ, μ′): μ, μ′ ∈ V(G) for any pair of vertices μ, μ′ in G. e span of labeling ℘ is the largest number that ℘ assigns to a vertex of a graph. Radio number of G, denoted by rn(G), is the minimum span taken over all radio labelings of G. In this article, we will find relations for radio number and radio mean number of a lexicographic product for certain families of graphs.
A fixing set F of a graph G is a set of those vertices of the graph G which when assigned distinc... more A fixing set F of a graph G is a set of those vertices of the graph G which when assigned distinct labels removes all the automorphisms from the graph except the trivial one. The fixing number of a graph G, denoted by f ix(G), is the smallest cardinality of a fixing set of G. In this paper, we study the fixing number of composition product, G 1 [G 2 ] and corona product, G 1 ⊙ G 2 of two graphs G 1 and G 2 with orders m and n respectively. We show that for a connected graph G 1 and an arbitrary graph G 2 having l ≥ 1 components G 1 2 , G 2 2 , ... G l 2 , mn − 1 ≥ f ix(G 1 [G 2 ]) ≥ m l i=1 f ix(G i 2). For a connected graph G 1 and an arbitrary graph G 2 , which are not asymmetric, we prove that f ix(G 1 ⊙ G 2) = mf ix(G 2). Further, for an arbitrary connected graph G 1 and an arbitrary graph G 2 we show that f ix(G 1 ⊙ G 2) = max{f ix(G 1), mf ix(G 2)}.
Journal of Mathematics, Dec 7, 2021
Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and... more Labeling of graphs has defined many variations in the literature, e.g., graceful, harmonious, and radio labeling. Secrecy of data in data sciences and in information technology is very necessary as well as the accuracy of data transmission and different channel assignments is maintained. It enhances the graph terminologies for the computer programs. In this paper, we will discuss multidistance radio labeling used for channel assignment problems over wireless communication. A radio labeling is a one-to-one mapping ℘: V(G) ⟶ Z + satisfying the condition |℘(μ) − ℘(μ′)| ≥ diam(G) + 1 − d(μ, μ′): μ, μ′ ∈ V(G) for any pair of vertices μ, μ′ in G. e span of labeling ℘ is the largest number that ℘ assigns to a vertex of a graph. Radio number of G, denoted by rn(G), is the minimum span taken over all radio labelings of G. In this article, we will find relations for radio number and radio mean number of a lexicographic product for certain families of graphs.