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On super mean labeling of some graphs
... The concept of over-defined flags was introduced and studied by D. Ramya et al. , [4]. R. Vasuki and A. Nagarajan [14] the upper average properties of the H-diagram of subdivisions and , some pips and subdivided graphs R. Vasuki. ...
This article presents a new method for encoding secret messages using super-intermediate symbols in star charts. The system includes two super average images and two formats, as well as graphics and matrix encoding methods for added security. The authors provide a method to adjust the average of the three star maps to ensure the stability of the encoded message. This research provides a non-programming method for developing matrix graphics coding techniques and has implications for fields such as telecommunications and cryptography. The use of super-average symbols and star charts provides a secure method of communication with applications in data encryption, network security, and confidential communication. The results of this study show that the effectiveness of the proposed system in improving the security and privacy of encrypted messages makes it useful in business.
... A graph that admits a super mean labeling is called a super mean graph. The concept of super mean labeling was introduced in [7] and further discussed in [2][3][4][5][6]. ...
Let G be a (p,q) graph and 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 prove that S(Pn ⊙K1),S(P2 ×P4 ),S(Bn,n),«Bn,n : Pm» ,Cn ⊙K2 ,n ≥3, generalized antiprism Amn and the double triangular snake D(Tn ) are 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.
Let G be a (p, q) graph and 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(y) + l)/2 if f(u) + f(v) is odd. Then f is called a super mean labeling if f(V) U {f*(e) : e ε E(G)} = {1,2,3,... ,p + q}. A graph that admits a super mean labeling is called a super mean graph. Let G be a (p, q) graph and f : V(G) → {1,2,3,... ,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) U {f* (e) : e ε E(G)} = {k, k + 1, k + 2,... ,p + q + k - 1}. A graph that admits a k-super mean labeling is called a k-super mean graph. In this paper we present super mean labeling of Cm U Cn and Tp-tree and also we construct some k-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.
Let G be a (p, q) graph and 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(y) + l)/2 if f(u) + f(v) is odd. Then f is called a super mean labeling if f(V) U {f*(e) : e ε E(G)} = {1,2,3,... ,p + q}. A graph that admits a super mean labeling is called a super mean graph. Let G be a (p, q) graph and f : V(G) → {1,2,3,... ,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) U {f* (e) : e ε E(G)} = {k, k + 1, k + 2,... ,p + q + k - 1}. A graph that admits a k-super mean labeling is called a k-super mean graph. In this paper we present super mean labeling of Cm U Cn and Tp-tree and also we construct some k-super mean graphs.
In this paper, we introduce a new type of graph labeling known as super mean labeling. We investigate the super mean labeling for the Complete graph K-n, the Star K-1,K-n ,the Cycle C2n+1,and the graph G(1) boolean OR G(2) where G(1) and G(2) are super mean graphs and some standard graphs.
The concept of super mean labeling was introduced by the authors. They investigate the super mean labeling of some standard graphs. In [M. A. Seoud and M. Z. Youssef, Ars Comb. 65, 155–176 (2002; Zbl 1071.05571)], harmonious graphs if order 6 were discussed. In the present paper, we determine all super mean graphs of order ≤5.
k -Super mean labeling of Graphs
- B Gayathri
- M Tamilselvi
- M Duraisamy
B.Gayathri, M.Tamilselvi and M.Duraisamy, k -Super mean labeling of
Graphs, Proceedings of the International Conference on Mathematics and
Computer Sciences, (2008),107-111.