Lucas graphs

Demırcı, Musa; Özbek, Aydın; Akbayrak, Osman; Cangül, İsmaıl Nacı

doi:10.1007/s12190-020-01382-z

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…In [5], the highest number of components of D is given as (5)…”

Section: Invariantmentioning

confidence: 99%

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Üçgensel sayılar ve graflar

Demırcı

2021

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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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 ≤ ≤ 4 .

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“…In [5], the highest number of components of D is given as (5)…”

Section: Invariantmentioning

confidence: 99%

“…Lucas graphs are defined as graphs with all the vertex degrees are consecutive Lucas numbers. In [5], the existence conditions for all Lucas graphs have been determined. In [7], the same search is done for Fibonacci numbers.…”

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confidence: 99%

Üçgensel sayılar ve graflar

Demırcı

2021

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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“…In [5,10], the Fibonacci and Lucas graphs have been studied and their existence conditions have been given. The general results obtained for the existence of Fibonacci and Lucas graphs of order n were given in modulo 3.…”

Section: Existence Conditions For Tribonacci Graphsmentioning

confidence: 99%

Tribonacci graphs

Demırcı

Cangül

2020

ITM Web Conf.

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Special numbers have very important mathematical properties alongside their numerous applications in many ﬁelds of science. Probably the most important of those is the Fibonacci numbers. In this paper, we use a generalization of Fibonacci numbers called tribonacci numbers having very limited properties and relations compared to Fibonacci numbers. There is almost no result on the connections between these numbers and graphs. A graph having a degree sequence consisting of t successive tribonacci numbers is called a tribonacci graph of order t. Recently, a new graph parameter named as omega invariant has been introduced and shown to be very informative in obtaining combinatorial and topological properties of graphs. It is useful for graphs having the same degree sequence and gives some common properties of the realizations of this degree sequence together with some properties especially connectedness and cyclicness of all realizations. In this work, we determined all the tribonacci graphs of any order by means of some combinatorial results. Those results should be useful in networks with large degree sequences and cryptographic applications with special numbers.

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