Omega Invariant of Complement Graphs and Nordhaus-gaddum Type Results
CURRENT ORGANIC SYNTHESIS, cilt.21, sa.3, ss.298-302, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 21 Sayı: 3
- Basım Tarihi: 2024
- Doi Numarası: 10.2174/1570179421666230914151600
- Dergi Adı: CURRENT ORGANIC SYNTHESIS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Biotechnology Research Abstracts, Chemical Abstracts Core, EMBASE, MEDLINE
- Sayfa Sayıları: ss.298-302
- Anahtar Kelimeler: complement of a graph, component, cyclomatic number, graph parameter, Omega invariant, triangular number
- Bursa Uludağ Üniversitesi Adresli: Evet
Özet
Aims: To obtain relations between the omega invariants of a graph and its complement. Background: We aim to use some graph parameters including the cyclomatic numbers, number of components, maximum number of components, order and size of both graphs G and (G) over bar. Also we used triangular numbers to obtain our results related to the cyclomatic numbers and omega invariants of.. and (G) over bar. Objective: Several bounds for the above graph parameters will be given by direct application of omega invariant. Methods: We use combinatorial and graph theoretical methods to study formulae, relations and bounds on the omega invariant, the number of faces and the number of components of all realizations of a given degree sequence. Especially so-called Nordhaus-Gaddum type results in our calculations. In these calculations, the number of triangular numbers less than a given number plays an important role. Quadratic equations and inequalities are intensively used. Several relations between the size and order of the graph have been utilized. Result: In this paper, we obtained relations between the omega invariants of a graph and its complement in terms of several graph parameters such as the cyclomatic numbers, number of components, maximum number of components, order and size of G and (G) over bar and triangular numbers. Conclusion: Some relations between the omega invariants of a graph and its complement are obtained.