Some general results on restricted k-mean graph

Advances in Mathematics: Scientific Journal, 2020

be a graph with p vertices and q edges. A(p, q)graph G is called an analytic even mean graph if there exist an injective function f : V → {0, 2, 4, 6, ..., 2q} with an induced edge labeling f * : E → Z such that when each edge e = uv with f (u) < f (v) is labeled with f * (uv) = f (v) 2 −(f (u)+1) 2 2 if f (u) = 0 and f * (uv) = f (v) 2 2 if f (u) = 0, all the edge labels are even and distinct. In this paper we show the analytic even mean labeling of coconut tree graph, fire cracker graph and some other results.

International Symposium on Algorithms and Computation, 2013

ARTICLE INFO Let G = (V, E) be a graph with p vertices and q edges. Let f : V → {0, 1, 2, • • • , k} (1 ≤ k ≤ q) be a vertex labeling of G that induces an edge labeling f * : E → {0, 1, 2, • • • , k} be given by f * (uv) = f (u)+ f (v) 2. A labeling f is called (k + 1)equitable mean labeling ((k + 1)-eml) if |v f (i) − v f (j)| ≤ 1 and |e f * (i) − e f * (j)| ≤ 1 for i, j = 0, 1, 2, • • • , k where v f (x) and e f * (x), x = 0, 1, 2, • • • , k are the number of vertices and edges of G respectively with label x. A new concept namely k-equitable mean labeling of a graph is introduced in this paper.

2019

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.

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.

ARTICLE INFO Let G = (V, E) be a graph with p vertices and q edges. Let f : V → {0, 1, 2, • • • , k} (1 ≤ k ≤ q) be a vertex labeling of G that induces an edge labeling f * : E → {0, 1, 2, • • • , k} be given by f * (uv) = f (u)+ f (v) 2. A labeling f is called (k + 1)equitable mean labeling ((k + 1)-eml) if |v f (i) − v f (j)| ≤ 1 and |e f * (i) − e f * (j)| ≤ 1 for i, j = 0, 1, 2, • • • , k where v f (x) and e f * (x), x = 0, 1, 2, • • • , k are the number of vertices and edges of G respectively with label x. A new concept namely k-equitable mean labeling of a graph is introduced in this paper.

International Journal of Mathematics Trends and Technology, 2014

Let G = (V, E) be a graph with p vertices and q edges and let f: V(G) → { 0, 1, 2, ...., q-1, q+1} be an injection. The graph G is said to have a near mean labeling if for each edge, there exist an induced injective map f * : E(G) → {1, 2, ...., q} defined by f * (uv) =     

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

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.

The graph theory is one of the field of discrete mathematics which cuts across wide range of disciplines of human understanding not only in the areas of pure mathematics but also in variety of application areas ranging from computer science to social sciences and in engineering to mention a few. The later part of last century has witnessed intense activity in graph theory. Developments of computer science boost up the research work in the field. There are many interesting fields of research in graph theory. Some of them are domination in graphs, coloring in graphs, topological graph theory, fuzzy graph theory and labeling of discrete structures. Graph theory has been instrumental for analyzing and solving problems in areas as diverse as computer network design, urban planning, and molecular biology. Graph theory has been used to find the best way to route and schedule airplanes and invent a secret code that no one can crack. A branch of mathematics is called a Graph Theory, a graph bears no relation to the graphs that chart data, such as the progress of the stock market or the growing population of the planet. Graph paper is particularly useful for drawing the graphs of Graph Theory. In Graph Theory, a graph is a collection of dots that may or may be connected to each other by lines. The principal object of the theory is a graph and its generalizations. The first problems in the theory of graphs were solutions of mathematical puzzles (the problem of the bridges of Konigsberg, the disposition of queens on a chessboard, transportation problems, the travelling-salesman problem, etc.). One of the first results in graph theory was a criterion on the possibility of traversing all edges of a graph without passing through any edge more than once; it was obtained by L. Euler in 1736 in solving the problem of the bridges of Konigsberg. The four-colour problem, formulated in the mid-19th century, though a mere amusement puzzle at first sight, led to studies of graphs of both theoretical and applied interest. Certain studies in the mid-19th century contain results of importance to graph theory, obtained by solving practical problems. Thus, G. Kirchhoffs complete set of equations for currents and voltages in electric circuits