Advances and Applications in Discrete Mathematics

The Advances and Applications in Discrete Mathematics is a prestigious peer-reviewed journal indexed in the Emerging Sources Citation Index (ESCI). It is dedicated to publishing original research articles in the field of discrete mathematics and combinatorics, including topics such as graphs, coding theory, and block design. The journal emphasizes efficient and powerful tools for real-world applications and welcomes expository articles that highlight current developments in the field.

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TOTALLY SEGREGATED POLYNOMIAL OF GRAPHS

Authors

  • Aziz B. Tapeing
  • Ladznar S. Laja
  • Javier Hassan
  • Hounam B. Copel

Keywords:

totally segregated graph, totally segregated polynomial.

DOI:

https://doi.org/10.17654/0974165823067

Abstract

A graph $G$ is totally segregated if $\operatorname{deg}_G(x) \neq \operatorname{deg}_G(y)$, whenever $x y \in E(G)$. The totally segregated polynomial of a graph $G$ of order $n$ is given by $T s(G, x)=\sum_{k=1}^n t(k) x^k$, where $t(k)$ is the number of totally segregated subgraphs of $G$ of order $k$. In this paper, characterizations of a totally segregated subgraph of a certain graph are provided. These characterizations are used to determine the totally segregated polynomials.

Received: September 21, 2023
Accepted: November 10, 2023

References

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T. F. Jorry, Minimum size of co-segregated graph, Advances and Applications in Discrete Mathematics 32 (2022), 91-112.

A. B. Tapeing and L. S. Laja, Co-segregated polynomial of graphs, Advances and Applications in Discrete Mathematics 40(1) (2023), 101-112.

Ladznar S. Laja and Rosalio G. Artes, Jr., Convex subgraphs polynomials of the join and composition of graphs, International Journal of Mathematical Analysis 10 (2016), 515-529.

P. M. Shivaswamy, Independent domination polynomial in graphs, IJSIMR 2(9) (2014), 755-763.

A. B. Tapeing and L. S. Laja, Co-segregated polynomial of graphs, Advances and Applications in Discrete Mathematics 40(1) (2023), 101-112.

A. Vijayan and T. Anitha, Connected total domination polynomials of graphs, International Journal of Mathematical Archive 5(11) (2014), 127-136.

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Published

2023-11-22

Issue

Vol. 40 No. 2 (2023)

Section

Articles

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How to Cite

TOTALLY SEGREGATED POLYNOMIAL OF GRAPHS. (2023). Advances and Applications in Discrete Mathematics, 40(2), 213-223. https://doi.org/10.17654/0974165823067

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