On Near 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 (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 A m n and the double triangular snake D(Tn) are super mean graphs.

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).

2019

Journal of Scientific Research, 2013

A graph) , (q p G = with p vertices and q edges is called a mean graph if there is an injective function f that maps V(G) to 3 2P K c n + are mean graphs.

A graph with p vertices and q edges is said to have an even vertex odd mean labeling if there exists an injective function f:V(G){0, 2, 4, ... 2q-2,2q} such that the induced map f*: E(G) {1, 3, 5, ... 2q-1} defined by f*(uv)=     f u f v 2  is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. In this paper we pay our attention for even vertex odd mean labeling graphs VD() , for any n and m , (), m,n

SUT Journal of Mathematics, 2010

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) = l f (u)+f (v) 2 m. 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.

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 A m n 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.

2013

A graph that admits a geometric mean labeling is called a geometric mean<br> graph. In this paper, we have discussed the geometric meanness of graphs obtained from some graph operations.

2017

In this paper, we prove that if m n   , then the three star 1, 1, 1, m n K K K   is a mean graph if and only if 1 4 m n m      when 1 9   and 8 4 m n m       when 9. 