Bounds for matching number of fundamental realizations according to new graph invariant Omega
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초록
Matching number of a graph is one of the intensively studied areas in graph theory due to numerous applications of the matching and related notions. Recently, Delen and Cangul defined a new graph invariant denoted by which helps to determine several graph theoretical and combinatorial properties of the realizations of a given degree sequence. In this paper, using K2 deletion process, the maximum and minimum matching numbers of all so-called fundamental realizations of a given degree sequence.
Abstract
Matching number of a graph is one of the intensively studied areas in graph theory due to numerous applications of the matching and related notions. Recently, Delen and Cangul defined a new graph invariant denoted by which helps to determine several graph theoretical and combinatorial properties of the realizations of a given degree sequence. In this paper, using K2 deletion process, the maximum and minimum matching numbers of all so-called fundamental realizations of a given degree sequence.
참고문헌 (19)
- Aigner, M, "Realizability and Uniqueness in Graphs", Discrete Math, 136, pp.3~20 (1994)
- Ashraf, F, "Energy, Matching Number and Odd Cycles of Graphs", Linear Algebra and its Applications, 577, pp.159~167 (2019)
- Barrus, M. D, "Neighborhood Degree Lists of Graphs", Discrete Math, 341, pp.175~183 (2018)
- Choudum, S. A, "On Forcibly Connected Graphic Sequences", Discrete Math, 96, pp.175~181 (1991)
- Delen, S, "A New Graph Invariant", Turkish Journal of Analysis and Number Theory, 6(1), pp.30~33 (2018)
- Delen, S, "Extremal Problems on Components and Loops in Graphs", Acta Mathematica Sinica, English Series, 35(2), pp.161~171 (2019)
- Delen, S, "Omega Invariant of Graphs and Cyclicness", Applied Sciences (2019)
- Guo, J.-M, "On the nullity and the matching number of unicyclic graphs", Linear Algebra and its Applications, 431(8), pp.1293~1301 (2009)
- Hakimi, S. L, "On the Realizability of a Set of Integers as Degrees of the Vertices of a Graph", J. SIAM Appl Math, 10, pp.496~506 (1962)
- Havel, V, "A Remark on the Existence of Finite Graphs (Czech)", Casopic Pest. Mat, 80, pp.477~480 (1955)
- Song, Y.-Z, "A characterization of graphs G with nullity |V(G)|=2m(G)+2c(G)", Linear Algebra and its Applications, 465, pp.363~375 (2015)
- Tam, B. S, "Nullities of Graphs with Given Order, Matching Number and Cyclomatic Number Revisited", Linear Algebra and its Applications, 535, pp.105~140 (2017)
- Triphati, A, "A short constructive proof of the Erdös-Gallai characterization of graphic lists", Discrete Math, 310, pp.843~844 (2010)
- Tyshkevich, R. I, "Graphs and degree sequences", Cybernetics, 23(6), pp.734~745 (1987)
- Wang, L, "Characterization of Graphs with Given Order, Given Size, Given Matching Number that Minimize Nullity", Discrete Mathematics, 339, pp.1574~1582 (2016)
- Wang, L, "Bounds for the matching number, the edge chromatic number and the independence number of a graph in terms of rank", Discrete Applied Mathematics, 166, pp.276~281 (2014)
- Wong, D, "Lower bounds of graph energy in terms of matching number", Linear Algebra and its Applications, 549, pp.276~286 (2018)
- Xuezhong, T, "On the nullity of unicyclic graphs", Linear Algebra and its Applications, 408, pp.212~220 (2005)
- Zverovich, I. E, "Contributions to the theory of graphic sequences", Discrete Math, 105, pp.293~303 (1992)