Analytic Odd Mean Labeling Of Some Standard Graphs

Palestine Journal of Mathematics, 2019

Keywords and phrases: mean labeling; analytic mean labeling; analytic odd mean labeling; analytic odd mean graph. is injective. We say that f is an analytic odd mean labeling of G. In this paper we prove that fan F n , double fan D(F n), double wheel D(W n), closed helm CH n , total graph of cycle T (C n), total graph of path T (P n), armed crown C n ΘP m , generalized peterson graph GP(n, 2) are analytic odd 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 to prove some graph operations of even vertex odd mean labeling graphs

Proyecciones (Antofagasta)

A graph G is analytic odd mean if there exist an injective function f : V → {0, 1, 3, . . . , 2q − 1} with an induced edge labeling f∗ : E → Z such that for each edge uv with f(u) < f(v), is injective. Clearly the values of f∗ are odd. We say that f is an analytic odd mean labeling of G. In this paper, we show that the union and identification of some graphs admit analytic odd mean labeling by using the operation of joining of two graphs by an edge.

A graph G with p vertices and q edges is a mean graph if there is an injective function f from the vertices of G to {0,1,2,….q} such that when each edge í µí±¢í µí±£ is labeled with í µí±“ í µí±¢ +í µí±“ í µí±£ 2 if í µí±“ í µí±¢ + í µí±“(í µí±£) is even and í µí±“ í µí±¢ +í µí±“ í µí±£ +1 2 if í µí±“ í µí±¢ + í µí±“(í µí±£) is odd then the resulting edges are distinct. In this paper we investigate vertex odd and even mean labeling of Umbrella graph , Mongolian tent and í µí°¾ 1 + í µí° ¶ í µí±› .

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.

Proyecciones Journal of Mathematics, 2023

A graph G is analytic odd mean if there exist an injective function f : V → {0, 1, 3,. .. , 2q − 1} with an induced edge labeling f * : E → Z such that for each edge uv with f (u) < f (v),

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)= () () fu fv 2 + is a bijection. A graph that admits an even vertex odd mean labeling is called an even vertex odd mean graph. Here we study the even vertex odd mean behaviour of H-graph.

2020

A graph G is a 2-odd graph if its vertices can be labeled with distinct integers such that for any two adjacent vertices, the absolute difference of their labels is either an odd integer or 2. In this paper, we investigate 2-odd labeling of various classes of graphs.

Journal of Fundamental Mathematics and Applications (JFMA), 2021

Let = ((), ()) be a connected graph with order | ()| = and size | ()| =. A graph is said to be even-to-odd mean graph if there exists a bijection function : () → {2, 4, 8, … , 2 } such that the induced mapping * : () → {3, 5, … , (2 − 1)} defined by * () = ()+ () 2 ∀ ∈ () is also bijective. The function is called an even-to-odd mean labeling of graph. This paper aimed to introduce a new technique in graph labeling called even-to-odd mean labeling. Hence, the concepts of even-to-odd mean labeling has been evaluated for some trees. In addition, we examined some properties of tree graphs that admits even-to-odd mean labeling and discussed some important results.

SUT Journal of Mathematics

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.