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Contra harmonic mean labeling of some graphs
... In graph labeling vertices or edges or both assigned values subject to the conditions. The "graceful labeling" introduced by Rosa (1967) [7] . J.A. Gallian [4] studied a complete survey on graph labeling.David.W. and Anthony. ...
The function (where is the Fibonacci number) is said to be Super Fibonacci graceful if the induced edge labeling defined by is bijective. In this paper an analysis is made on Friendship graph, Butterfly graph , The graph-and the graph obtained by attaching a triangle at each pendant vertex of a Star graph,(3,n)-kite graph under Super Fibonacci graceful labeling .
... In graph labeling vertices or edges or both assigned values subject to the conditions. The "graceful labeling" introduced by Rosa (1967) [7] . J.A. Gallian [4] studied a complete survey on graph labeling.David.W. and Anthony. ...
The function (where is the Fibonacci number) is said to be Super Fibonacci graceful if the induced edge labeling defined by is bijective. In this paper an analysis is made on Friendship graph, Butterfly graph , The graph-and the graph obtained by attaching a triangle at each pendant vertex of a Star graph,(3,n)-kite graph under Super Fibonacci graceful labeling .
... By the definition of the Butterfly graph, the vertex set V(G)={ 1 , 2 , 3 , 4 , 5 , 1 , 2,…, }. Let 1 , 2 , 3 , 4 , 5 be the vertices of the two cycles 3 and 1 be the apex vertex of the two cycles 3 ...
The Fibonacci series is utilized to produce Fibonacci in a recursive grouping.
... Some Results on Contra Harmonic Mean Labeling of Graphs obtained in [13] and Anti-magic labeling for Boolean graph of path ( ), ( 4) n BG P n is obtained in [16]. ...
... In [4], Somasundaram and Ponraj introduced and studied mean labeling for some standard graphs. Somasundaram et al. [5], [7] introduced Harmonic mean labeling of graphs. Somasundaram et al. [6] introduced the concept of Geometric mean labeling of graphs and studied their behaviour. ...
... S.S. Sandhya and S. Somasundaram introduced Harmonic mean labeling of graph. We have introduced Contra Harmonic mean labeling in [5].The Contra Harmonic mean labeling of disconnected graphs are introduced in [6]. In this paper we investigate the Contra Harmonic mean labeling behaviour of some more disconnected graphs. ...
... In graph labeling vertices or edges or both assigned values subject to the conditions. The "graceful labeling" introduced by Rosa (1967) [7] . J.A. Gallian [4] studied a complete survey on graph labeling.David.W. and Anthony. ...
... In graph labeling vertices or edges or both assigned values subject to the conditions. The "graceful labeling" introduced by Rosa (1967) [7] . J.A. Gallian [4] studied a complete survey on graph labeling.David.W. and Anthony. ...
The function
(where is the Fibonacci number) is said to be
Super Fibonacci graceful if the induced edge labeling
defined by
is bijective. In this paper an analysis is
made on Friendship graph, Butterfly graph , The
graph – and the graph obtained by attaching
a triangle at each pendant vertex of a Star
graph,(3,n)-kite graph under Super Fibonacci graceful
labeling .
Consider the graph G, with the injection Ω from node set to the first p + q natural numbers. Let us assume that the ceiling function of the classical average of the node labels of the end nodes of each link is the induced link assignment Ω *. If the union of range of Ω of node set and the range of Ω * of link set is all the first p + q natural numbers, then Ω is called a classical mean labeling. A super classical mean graph is a graph with super classical mean labeling. In this research effort, we attempted to address the super classical meanness of graphs generated by paths and those formed by the union of two graphs.
Numbering a graph is a very practical and effective technique in science and engineering. Numerous graph assignment techniques, including distance-based labeling, topological indices, and spectral graph theory, can be used to investigate molecule structures. Consider the graph G , with the injection Ω from the node set to 1 , 2 , … , ∆ , where ∆ is the sum of the number of nodes and links. Assume that the induced link assignment Ω ∗ is the ceiling function of the average of root square, harmonic, geometric, and arithmetic means of the vertex labels of the end vertices of each edge. If the union of range of Ω of the node set and the range of Ω of the link set is the set 1 , 2 , … , ∆ , then Ω is called a super classical average assignment (SCAA). This is known as the SCAA criterion. In this study, the graphical structures corresponding to chemical structures based on the SCAA criterion are demonstrated. The graphical depiction of chemical substances was first defined and second, the union of any number of cycles C n , the tadpole graph, the graph extracted by identifying a line of any two cycles C m and C n , and the graph extracted by joining any two cycles by a path are all examined in this work.
Classical mean labeling of a graph G with p vertices and q edges is an injective function from the vertex set of G to the set 1, 2, 3,. .. , q + 1 such that the edge labels obtained from the ooring function of the average of mean of arithmetic, geometric, harmonic, and root square of the vertex labels of each edge's end vertices is distinct, and the set of edge labels is 1, 2, 3,. .. , q. One of the graph operations is to duplicate the graph. e classical meanness of graphs formed by duplicating an edge and a vertex of numerous standard graphs is discussed in this study.
We propose a new puzzle: Label the eight vertices of a cube using distinct integers between 0 and 12 (both inclusive) such that the induced labeling of each edge, given by the sum of the labels of its end points, causes the 12 edges to be labeled with distinct odd numbers 1, 3, … 23.
Any solution to the puzzle is called a super odd-sum labeling. We deftly discover all the super odd-sum labeling of the cube.
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