Edge geodetic sequence in graphs

Document Type : Research Paper

Authors

1 Department of Mathematics, St. Alphonsa College of Arts and Science Karunkal, Tamil Nadu, India.

2 Department of Mathematics, Government College of Engineering Tirunelveli, Tamil Nadu, India.

Abstract

In this paper, we introduced the concept of edge geodetic sequences in graph and its generating function. Some general properties satisfied by this concept are studied. It is shown that for every generating function
$$ G(x)=\sum_{i=1}^{\infty} {a}^{i-1}{x^{i-1}} \quad a\in N-\left\lbrace 1\right\rbrace,$$
there exists a recurrence graph $G$ with edge geodetic decomposition $\pi=\{G_{1},G_{2},\ldots ,G_{n}\ldots\}$.

Keywords

References

[1] H. A. Ahangar and M. Najimi, Total restrained geodetic number of graphs, Iran. J. Sci. Technol. Trans. A Sci., 41 No. 2 (2017) 1-8.
[2] D. A. Mojdeh and N. Jafari Rad, Connected geodomination in graphs, J. Discrete Math. Sci. Cryptogr., 9 No. 1 (2006) 177-186.
[3] F. Harary, Graph Theory, Narosa Publishing House, 1998.
[4] J. John and D. Stalin, Edge geodetic self decomposition in graphs, Discrete Math. Algorithms Appl., 12 No. 05 (2020) 2050064.
[5] J. John and D. Stalin, The edge geodetic self decomposition number of a graph, RAIRO Oper. Res., 55 (2021) S1935 - S1947.
[6] J. John and D. Stalin, Distinct edge geodetic decomposition in graphs, Commun. Comb. Optim., 6 No. 2 (2021) 185-196.
[7] P. Paulraja and T. Sivakaran, Decompositions of some regular graphs into unicyclic graphs of order five, Discrete Math. Algorithms Appl., 11 (2019) 1950042.
[8] A. P. Santhakumaran and J. John, Edge geodetic number of a graph, J. Discrete Math. Sci. Cryptogr., 10 No. 3 (2007) 415-432.
[9] V. Samodivkin, On the edge geodetic and edge geodetic domination numbers of a graph, Commun. Comb. Optim., 5 No. 1 (2019) 41-54.
Algebraic Structures and Their Applications
Volume 11, Issue 3
August 2024
Pages 195-208

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