Super Mean Research Articles

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.

Parabolic super mean value inequality

In this note, we show that a type of mean value inequality for the positive supersolutions to the heat equation on a Riemannian manifold is equivalent to a version of local heat kernel lower bounds. We also show that the global Gaussian type heat kernel lower bound implies that the manifold has the Liouville property.