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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CONNECTED TOTAL DOMINATING NEIGHBORHOOD POLYNOMIAL OF GRAPHS

Authors

  • Rosalio G. Artes Jr.
  • Rashidin H. Moh. Jiripa
  • Jeffrey Imer C. Salim

Keywords:

dominating set, connected total dominating set, neighborhood system, connected total dominating neighborhood polynomial

DOI:

https://doi.org/10.17654/0974165823042

Abstract

In this study, we introduce a concept of connected total dominating neighborhood polynomial of a graph and establish relationships between the algebraic properties of this polynomial and the graph-theoretic properties of the neighborhood system of a connected total dominating set of a graph. Moreover, certain results on the connected total dominating neighborhood polynomials of some special graphs such as complete graphs, complete bipartite graphs, and complete q-partite graphs have been obtained.

References

S. Alikhani and Y. Peng, Introduction to domination polynomial of a graph, Ars Combin. 114 (2014), 257-266.

R. G. Artes, Jr., M. A. Langamin and A. B. Calib-og, Clique common neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 35 (2022), 77-85.

J. A. Bondy and U. S. R. Murty, Graph Theory and Related Topics, Academic Press, New York, 1979.

J. Brown and R. Nowakowski, The neighborhood polynomial of a graph, Australas. J. Combin. 42 (2008), 55-68.

B. Chaluvaraju and V. Chaitra, Total domination polynomial of a graph research article, Journal of Informatics and Mathematical Sciences 6(2) (2014), 87-92.

J. Ellis-Monaghan and J. Merino, Graph Polynomials and their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011.

G. M. Entero and A. C. Pedrano, On connected total domination polynomial of some lexicographical product graphs, Advances and Applications in Discrete Mathematics 27(1) (2021), 147-155.

J. L. Gross and J. Yellen, Graph Theory and its Applications, Chapman & Hall, New York, 2006.

I. Gutman, Graphs and graph polynomials of interest in chemistry, Gottfried Tinhofer and Gunther Schmidt, eds., Lecture Notes in Computer Science, Springer-Verlag, Berlin, 2005, pp. 177-187.

F. Harary, Graph Theory, CRC Press, Boca Raton, 2018.

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Published

2023-05-23

Issue

Vol. 39 No. 2 (2023)

Section

Articles

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Copyright (c) 2023 PUSHPA PUBLISHING HOUSE, PRAYAGRAJ, INDIA

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How to Cite

CONNECTED TOTAL DOMINATING NEIGHBORHOOD POLYNOMIAL OF GRAPHS. (2023). Advances and Applications in Discrete Mathematics, 39(2), 145-154. https://doi.org/10.17654/0974165823042

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