Soumya Ranjan’s scientific contributions

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Figure 2 Triangular Graph Let and be the vertices and and are edges of the graph , as illustrated in Figure 2. Define the the unique mapping function as follows and . Define a edge function such as is bijection. The edge values are defined by and . Therefore . So is Uniform(even) Vertex odd Mean Labeling. A graph that admits Uniform(even) Vertex odd Mean Labeling is a Uniform(even) Vertex odd Mean Labeling graph. Theorem 3: An alternate triangular snake graph satisfies Uniform(even) Vertex odd Mean Labeling. Proof: Let be a graph with are the vertices and are the edges of the graph as illustrated in Figure 3
Figure 3 Alternate triangular snake Graph Define the the unique mapping function as follows and the edges function defined by as follows is a bijection function. The edge values are . Hence .
Figure 4 Caterpillar Graph Define the unique mapping function as follows
Figure 5 Graph
Figure 6 Double alternate triangular graph
© Even vertex odd mean labeling of some graphs
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January 2024

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61 Reads

Journal of Discrete Mathematical Sciences and Cryptography

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S Vidyanandini

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Soumya Ranjan

This work introduces the principle of “an even point (vertex) odd ratio (mean) labeling, which is specifically applied to a graph ‘G’ consisting of ‘p’ vertices and ‘q’ edges. Even point (vertex) odd ratio (mean) labeling is exhibited by a graph G in the presence of an injectionbased function f : V of G → {0, 2, 4, ... 2q – 2, 2q} ensuring that the function derived from it (induced map) g* : E of G→{1, 3, 5, ... 2q – 1} specified by g* (uv) = g(u)+g(v)/2 is a bijection. Graphs that meet these criteria are termed an even point (vertex) odd ratio (mean) graphs. This paper explores the properties of an even point (vertex) odd ratio (mean) labeling in various graph structures.

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