Super Mean Labeling Research Articles

Coding Technique With Two and Three Stars, SSML(N4,L2) and GMJ CODE

In this paper, we introduce a coding technique for converting a text message using sub super mean labeling on two and three star graphs to a picture coding message. The first part of this paper there are some definitions and discussions for the existence graph and in the second part there are some illustrations to explain how the text message is converted in to picture code, by using graph labeling, and it maintain secrecy, possess intricacy and provide a sense of sufficiency. Secrecy is the practice of hiding information from certain individuals or groups who do not have the need to know, perhaps while sharing it with other individuals that which is kept hidden is known as secret.

A method of sharing secrecy using star graphs

This article introduces a new technique of picture coding method for a secret text messages in the form of matrix using star related graphs by applying the subset of super mean labeling, sub super mean labeling is one of the important topics in graph theory. Let G be a (p, q) graph and α : V (G) → {1, 2, 3, · · ·, p+q} be an injection. For each edge l = uv, let then α is called Sub Super Mean Labeling if α(V) U {α*(l) : l G E(G)} C {one, two, three, · · ·, p+q}. A graph that admits a Sub Super Mean Labeling is called a Sub Super Mean Graph.

An application of super mean and magic graphs labeling on cryptography system

An edge-magic total (EMT) labeling on a simple graph G with p vertices and q edges is a bijection f: V∪E→{1, 2, …, p + q} such that for each edge xy of G, f(x) + f(xy) + f(y) = k, for a fixed positive integer k. Moreover, an EMT labeling f is a super edge-magic total labeling (SEMT) if f(V) = {1, 2, …, p}. Furthermore, a graph G is called a super mean (SM) graph if there exists an injective function f from the vertices of G to {0,1,2,…,q} such that when each edge uv is labeled with (f(u) +f(v))/2 when f(u) +f(v) is even, and (f(u) +f(v) + 1)/2 when f(u) +f(v) is odd, then the resulting edge labels are distinct. There are two essentials results that will be proposed in this paper. In the first result, we show that a graph (n, 1) − F Caterpillar has a SM labeling and a graph Hu,y has a SEMT labeling. In the second result, we will give an application of these labeling to increase the security level of Affine Cipher in which to encrypt a text on socials media.

Existence and Non-Existence of Super Mean Labeling on Star Graphs

Existence and Non-Existence of Super Mean Labeling on Star Graphs

Cordial, 1-near mean cordial \& super mean labeling of tensor product of paths

Cordial, 1-near mean cordial \& super mean labeling of tensor product of paths

A study on M-joins of super mean labeling of some digital numbers

A study on M-joins of super mean labeling of some digital numbers

Coding through on the disconnected graph $nK_{1, m}$, $n > 1$ a super mean labeling graph

Coding through on the disconnected graph $nK_{1, m}$, $n > 1$ a super mean labeling graph

A comprehensive study of super mean labelling in three star graph

Here our discussion is on a three star graph which is finite, simple and undirected one. For notations and terminology, we follow [1]. The vertex set and the edge set of a graph G are denoted by V (G) and E (G) respectively. So G(V,E) is a graph with p vertices and q edges. Much work is done by researchers on Mean labeling and Super mean labeling of graphs applying them on a variety of graphs [2-7,9,10]. Motivated by these work the concept of SSML(V4,E2) on a two star graph was introduced by Uma Maheshwari et al [8]. After a discussion on SSML(V4,E2) on a two star graphs, we were inspired to apply SSML(V4,E2) on three star graphs and hence this paper. Here the word sub is used thereby allowing omissions which lead to repetitions and a special case SSML(V4,E2). A study on omissions and repetitions on a three star graphs is done which admits SSML(V4,E2) and the formula is obtained in terms of, mand n in this paper.

On Super Mean Labeling for Total Graph of Path and Cycle

Let G(V,E) be a graph with the vertex set V and the edge set E, respectively. By a graph G=(V,E) we mean a finite undirected graph with neither loops nor multiple edges. The number of vertices of G is called order of G and it is denoted by p. Let G be a (p,q) graph. A super mean graph on G is an injection f:V→{1,2,3…,p+q} such that, for each edge e=uv in E labeled by f⁎e=fu+f(v)/2, the set fV∪{f⁎e:e∈E} forms 1,2,3,…,p+q. A graph which admits super mean labeling is called super mean graph. The total graph T(G) of G is the graph with the vertex set V∪E and two vertices are adjacent whenever they are either adjacent or incident in G. We have showed that graphs T(Pn) and TCn are super mean, where Pn is a path on n vertices and Cn is a cycle on n vertices.

New classes of super geometric mean graphs

Let f : V(G) →{1, 2, … , p+q} be an injective function. For a vertex labeling “f” the induced edge labeling f*(e=uv) is defined by, . Then “f” is called a Super Geometric mean labeling” if {f(V(G))}∪{(f(e) : e∈E(G)}={1, 2, … , p+q}. A graph which admits Super Geometric mean labeling is called “Super Geometric mean graph”.In this paper, we prove that TLn, TLnAK1 TnAK1, QnAK1 and [A(Tn)]AK1 and [A(Qn)]AK1 are Super Geometric mean graphs.

New super mean graphs

Let G(V, E) be a graph with p vertices and q edges and f: V(G) → {1,2,3,…, p + q} be an injection. For each edge e = uv, let . Then f is called a super mean labeling of G if {f (V(G)) ∪ {f *(e): e ∊ E(G)} = {1,2,3,…, p + q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we prove that , , , T @ Pn, T @ 2Pn, are super mean graphs if T is a Tp -tree.

Super Mean Labeling of Some Classes of Graphs

Super Mean Labeling of Some Classes of Graphs

Further results on super mean graphs

Let G be a graph and f : V(G) → {1, 2, 3, …, p + q} be an injection. For each edge e = uv, the induced edge labeling f* is defined as follows: Then f is called super mean labeling if f(V(G)) ∪ {f*(e): e ∈ E(G)} = {1, 2, 3, …, p + q}. A graph that admits a super mean labeling is called super mean graph. In this paper we study the super meanness of subdivision graph of K 1,3, super meanness of Pτ,4, super meanness of some caterpillars and super meanness of some duplicate graphs.

On the construction of new classes of super mean graphs

Let G be a (p, q) graph and f : V(G) → {1, 2, 3,…, p + q} be an injection. For each edge e = uv, the induced edge labeling f* is defined as follows: Then f is called super mean labeling if f (V(G)) ∪ {f* (e) : e ∈ E(G)} = {1, 2, 3,…, p + q}. A graph that admits a super mean labeling is called super mean graph. In this paper, we discuss the construction of two kinds of super mean graphs. Here we prove that (Pm ; Cn )n ≥ 3 and n = 4, (P 2n ; Sm )m ≥ 1, n ≥ 1, [Pm ; Cn ]n ≥ 3 and n ≠ 4, [P 2n ; Sm ]m ≥ 1, n ≥ 1 and , m ≥ 1, n ≥ 3 and n ≠ 4 are super mean graphs. Also we establish that union of any number of super mean graph is a super mean graph.

On super mean labeling of some graphs

Let G be a (p,q)-graph and : V(G)→{k,k+1,k+2,k+3,…,p+q+k−1} be an injection. For each edge e=uv, let f*(e)=⌈ f(u)+f(v)2 ⌉. Then f is called a k-super mean labeling if f(V)∪{f*(e):e∈E(G)}={k,k+1,k+2,…,p+q+k−1}. A graph that admits a k-super mean labeling is called k-super mean graph. In this paper, we present k-super mean labeling of C2n(n≠2) and super mean labeling of Double cycle C(m,n), Dumb bell graph D(m,n) and Quadrilateral snake Qn.

On Super mean graphs

Let G be a (p, q) graph and let f: V(G) → {1, 2, 3,…, p + q} be an injection. For each edge e = uv, let f*(e) = (f(u)+f(v))/2 if f(u)+f(v) is even and f* (e) = (f(u)+f(v)+1)/2 if f(u)+f(v) is odd. Then f is called a super mean labeling if f(V) ≼ {f* (e): e ∊ E(G)} = {1, 2, 3,…, p + q}. A graph that admits a super mean labeling is called a super mean graph. In this paper we present several infinite families of super mean graphs.