CONVEX INDEPENDENT COMMON NEIGHBORHOOD POLYNOMIAL OF A GRAPH
We introduce the concept of convex independent common neighborhood polynomial of a graph and determine the convex independent common neighborhood polynomials of some special graphs such as paths, cycles, complete graphs, and complete bipartite graphs.
convex set, independent set, common neighborhood system, convex independent common neighborhood polynomial.
Received: January 21, 2023; Accepted: March 15, 2023; Published: April 11, 2023
How to cite this article: Amelia L. Arriesgado and Rosalio G. Artes, Jr., Convex independent common neighborhood polynomial of a graph, Advances and Applications in Discrete Mathematics 38(2) (2023), 145-158. http://dx.doi.org/10.17654/0974165823025
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References:
[1] N. Abdulcarim, S. Dagondon and E. Chacon, On the independent neighborhood polynomial of the Cartesian product of some special graphs, European Journal of Pure and Applied Mathematics 14(1) (2021), 173-191.[2] R. Artes and L. Laja, Zeros of convex subgraph polynomials, Applied Mathematical Sciences 8(59) (2014), 2917-2923.[3] R. Artes, M. Langamin and A. Calib-og, Clique common neighborhood polynomial of graphs, Advances and Applications in Discrete Mathematics 35 (2022), 77-85.[4] R. Artes and M. J. Luga, Convex accessibility in graphs, Applied Mathematical Sciences 8(88) (2014), 4361-4366.[5] J. A. Bondy and USR Murty, Graph Theory and Related Topics, Academic Press, New York, 1979.[6] J. Brown and R. Nowakowski, The neighborhood polynomial of a graph, Australasian Journal of Combinatorics 42 (2008), 55-68.[7] J. Ellis-Monaghan and J. Merino, Graph Polynomials and Their Applications II: Interrelations and Interpretations, Birkhauser, Boston, 2011.[8] J. L. Gross and J. Yellen, Graph Theory and its Applications, Chapman & Hall, New York, 2006.[9] I. Gutman, Graphs and graph polynomials of interest in chemistry, In Gottfried Tinhofer and Gunther Schmidt, editors, Lecture Notes in Computer Science, Berlin, Springer-Verlag, 2005, pp. 177-187.[10] F. Harary, Graph Theory, CRC Press, Boca Raton, 2018.[11] C. Hoede and X. Li, Clique polynomials and in dependent set polynomials of graphs, Discrete Mathematics 125 (1994), 219-228.
