On Construction of 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.

viXra, 2010

A graph that admits a Smarandachely near mean m-labeling is called Smarandachely near m-mean graph. The graph that admits a near mean labeling is called a near mean graph (NMG). In this paper, we proved that the graphs Pn, Cn,K2,n are near mean graphs and Kn(n > 4) and K1,n(n > 4) are not near mean graphs.

ijpam.eu

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. 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) ∪ {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 a k-super mean graph. In this paper we present super mean labeling of C m ∪ C n and T p-tree and also we construct some k-super mean graphs.

SUT Journal of Mathematics

Let G be a graph and f : V (G) → {1, 2, 3,. .. , p + q} be an injection. For each edge uv, the induced edge labeling f * is defined as f * (uv) = ⌈ √ f (u)f (v) ⌉. Then f is called a super geometric mean labeling if f (V (G)) ∪ {f * (uv); uv ∈ E(G)} = {1, 2, 3,. .. , p + q}. A graph that admits a super geometric mean labeling is called a super geometric mean graph. In this paper, we discuss the super geometric meanness of union of any paths, union of any cycles of order ≥ 5, the graph Pn ⊙Sm for m ≤ 3, square graph, total graph, the H-graph, the graph G ⊙ S1 and G ⊙ S2 for any H-graph G, subdivision of K1,3 and some chain graphs.

Let G = (V,E) be a graphs with p vertices and q edges. An Extended Mean Cordial Labeling of a Graph G with vertex set V is a bijection from V to {-1,0,1} such that each edge uv is assigned the label (|f(u)+f(v)|)/2 where |x| is the least integer greater than or equal to x with the condition that the number of vertices labeled with 0 and the number of vertices labeled with 1 differ by at most 1 and the number of edges labeled with 0 and the number of edges labeled with 1 differ by almost 1. The graph that admits an Extended Mean Cordial Labeling is called Extended Mean Cordial Graph. In this paper, we proved that special graphs(umbrella), Q(n),(í µí±ƒ í µí±› : í µí° ¶ 3) are Extended Mean Cordial Graphs.

International Journal of Mathematical Combinatorics, 2019

A graph G = (V, E) with p vertices and q edges is said to have centered triangular mean labeling if it is possible to label the vertices x ∈ V with distinct elements f (x) from S, where S is a set of non-negative integers in such a way that for each edge e = uv, f * (e) = f (u)+f (v) 2 and the resulting edge labels are the first q centered triangular numbers. A graph that admits a centered triangular mean labeling is called centered triangular mean graph. In this paper, we prove that the graphs Pn,

2016

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 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 Super mean graph. Let G be a (p, q) graph and f:V G → k,k + 1,k + 2,... ,p + q + k − 1 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 k-super mean labeling if f V ∪ f e :e ∈ E(G) = {k,k + 1, . . ,p + q + k − 1}. A graph that admits a k-super mean labeling is called k-Super mean graph. In this paper we investigate k – super mean labeling of Hn, Hn ⊙mK1, A(DTn), n P1 ⊙K2 and KP(r, s, l).

Journal of Algorithms and Computation, 2018

A graph G is said to be one modulo three geometric mean graph if there is an injective function φ from the vertex set of G to the set {a | 1 ≤ a ≤ 3q − 2} and either a ≡ 0(mod3) or a ≡ 1(mod3)} where q is the number of edges of G and φ induces a bijection φ * form the edge set of G to {a | 1 ≤ a ≤ 3q − 2 and a ≡ 1(mod3)} given by φ * (uv) = φ(u)φ(v) or φ(u)φ(v) and the function φ is called one modulo three geometric mean labeling of G. In this paper, we establish that some families of graphs admit one modulo three geometric mean labeling.

SUT Journal of Mathematics, 2011

Let G be a (p,q)-graph and f: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. We present k-super mean labeling of C 2n (n≠2) and super mean labeling of double cycle C(m,n), dumb bell graph D(m,n) and quadrilateral snake Q n .

American Journal of Applied Mathematics and Statistics, 2014

In this paper, we introduce a new labeling called one modulo three mean labeling. A graph G is said to be one modulo three mean graph if there is an injective function φ from the vertex set of G to the set {a | 0 ≤ a ≤ 3q-2 and either a≡0(mod 3) or a≡1(mod 3) } where q is the number of edges of G and φ induces a bijection φ * from the edge set of G to { } one modulo three mean labeling of G. Furthermore, we prove that some standard graphs are one modulo three mean graphs.