Omega Invariant of Union, Join and Corona Product of Two Graphs
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초록
Graphs nowadays are getting a lot of attention due to their applications in all areas of science including physics, chemistry, pharmacology, network science, neuroscience, social sciences, etc. There are several mathematical methods used in graph theory to obtain such applications. Nearly in half of them, the vertex degrees and the degree sequences play an important role. The graph products are very useful tools as they help us to calculate several properties of large graphs by means of smaller graphs. Recently, a new topological graph invariant named as omega was defined in terms of the vertex degrees, that is degree sequence. In this paper, the degree sequences of the union of some special graph classes are given. Recalling the degree sequences of the join and corona products of two special graph classes from literature, the omega invariants of the union, join and corona products of two special graphs are obtained. Also for each of these graph products, results giving the omega values and the number of faces for general graphs are given.
Abstract
Graphs nowadays are getting a lot of attention due to their applications in all areas of science including physics, chemistry, pharmacology, network science, neuroscience, social sciences, etc. There are several mathematical methods used in graph theory to obtain such applications. Nearly in half of them, the vertex degrees and the degree sequences play an important role. The graph products are very useful tools as they help us to calculate several properties of large graphs by means of smaller graphs. Recently, a new topological graph invariant named as omega was defined in terms of the vertex degrees, that is degree sequence. In this paper, the degree sequences of the union of some special graph classes are given. Recalling the degree sequences of the join and corona products of two special graph classes from literature, the omega invariants of the union, join and corona products of two special graphs are obtained. Also for each of these graph products, results giving the omega values and the number of faces for general graphs are given.
참고문헌 (8)
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- V. N., Mishra, "Degree Sequences of Join and Corona Products of Graphs", Electronic Journal of Analysis and Applications, 7(1), pp.5~13 (2019)
- W. D. Wallis, "A Beginner’s Guide to Graph Theory" (2007), Birkhauser
- D. B. West, "Introduction to Graph Theory" (2001), Pearson