A Novel Approach to C_exp Average Assignments on Chain Graphs

Authors

A. Rajesh Kannan, Department of Mathematics, Mepco Schlenk Engineering College (Autonomous), Sivakasi - 626 005, Tamil Nadu, India.Follow

Abstract

In general, the exponential average of two positive numbers does not have to be an integer. Because of this, the exponential average needs to be an integer that takes into consideration the flooring or ceiling function. It has been defined that graphs can be labeled with an exponential average, where the flooring function or the ceiling function can apply labels to the edges. To establish the exponential average assignment on graphs, consider the edge labels that arise from the ceiling function alone. The vertex assignment function 𝛿 and edge assignment function 𝛿∗ are called a Cexp average assignment of the graph G with p vertices and q edges if 𝛿 is injective and 𝛿∗is bijective and the corresponding relations are 𝛿:𝑉→𝛮−{𝑞+2,⋯,∞},𝛿∗:𝐸→𝛮−{1,𝑞+2,⋯,∞} and is defined by edge label 𝛿∗ is 𝛿∗(𝑢𝑣)=⌈1𝑒(𝑋(𝑣)𝑋(𝑢))1𝑌(𝑢,𝑣)⌉ where 𝑋(𝑢)=𝛿(𝑢)𝛿(𝑢),𝑌(𝑢,𝑣)=𝛿(𝑣)−𝛿(𝑢) and N is the set of all natural numbers. If the graph accepts a Cexp average assignment then it is called a Cexp average assignment graph. The Cexp average assignment of graphs is proposed in this paper, and its characteristics are explored on the cycle, the union of path and cycle, the union of T- graph and cycle, the graph G*, the graph G′, the graph Ĝand tadpole.

Keywords

Cexp average assignment, Cexp average assignment graph, Chain graphs, Edge labeling, Vertex labeling.

Subject Area

Mathematics

Article Type

Article

First Page

1317

Last Page

1323

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite this Article

Kannan, A. Rajesh (2025) "A Novel Approach to C_exp Average Assignments on Chain Graphs," Baghdad Science Journal: Vol. 22: Iss. 4, Article 24.
DOI: https://doi.org/10.21123/bsj.2024.11034