### Triangular numbers and graphs

Musa Demirci

#### Öz

Graphs have applications in all areas of science and therefore the interest in Graph Theory is increasing everyday.  They have applications in Chemistry, Pharmacology, Anthropology, Biology, Network Sciences etc.  In this paper, Graph theory is connected with algebra by means of a new graph invariant Ω and define triangular graphs as graphs with a degree sequence consisting of n successive triangular numbers and use Ω and its properties to give a characterization of them. We give the conditions for the realizability of a set D of n consecutive triangular numbers and also give all possible graphs for 1≤t≤4 .

#### Anahtar Kelimeler

Omega invariant; degree sequence; triangular number; triangular graph

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#### Referanslar

Delen, S., Cangül, İ.N., A new graph invariant, Turkish Journal of Analysis and Number Theory, 6 (1), 30-33, (2018).

Delen, S., Cangül, İ.N., Extremal problems on components and loops in graphs, Acta Mathematica Sinica, English Series, 35 (2), 161-171, (2019).

Delen, S., Togan, M., Yurttas, A., Ana, U., Cangül, İ.N., The effect of edge and vertex deletion on omega invariant, Applicable Analysis and Discrete Mathematics, Special Issue, vol. II, (2020).

Delen, S., Yurttas, A., Togan, M., Cangül, İ.N., Omega invariant of graphs and cyclicness, Applied Sciences, 21, 91-95, (2019)

Demirci, M., Özbek, A., Akbayrak, O., Cangül, İ. N., Lucas graphs, Journal of Applied Mathematics and Computation, DOI: 10.1007/s12190-020-01382-z, (2020).

Şanlı, U., Çelik, F., Delen, S., Cangul, İ. N., Connectedness criteria for graphs by means of omega invariant, FILOMAT, (2020) (Prepirint).

Yurttaş Güneş, A., Delen, S., Demirci, M., Çevik, A. S., Cangül, İ. N., Fibonacci graphs, Symmetry, 12, 1383, (2020).

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Telif Hakkı (c) 2020 Musa Demirci