Extremal Problems on Components and Loops in Graphs

Delen, Sadik; Cangül, İsmaıl Nacı

doi:10.1007/s10114-018-8086-6

Cited by 14 publications

(15 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For convenience, the omega invariant of a realization G of D is also denoted by Ω( ). Some properties of Ω can be found in [1,2,3,4,6]. We recall some very important properties of it here.…”

Section: Invariantmentioning

confidence: 99%

See 1 more Smart Citation

Üçgensel sayılar ve graflar

Demırcı

2021

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

View full text Add to dashboard Cite

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 .

show abstract

Section: Invariantmentioning

confidence: 99%

“…A degree sequence is = {1 ( 1 ) , 2 ( 2 ) , 3 ( 3 ) , . .…”

Section: Introductionmentioning

confidence: 99%

Üçgensel sayılar ve graflar

Demırcı

2021

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

View full text Add to dashboard Cite

show abstract

“…In [6], some extremal problems on the numbers of components and loops of all realizations of a given degree sequence were given. We now apply this new invariant Ω to Bell irregularity index.…”

Section: Theorem 25 ([5]) Letmentioning

confidence: 99%

Inverse problem for Bell index

Togan

Yurttas

Sanli

et al. 2020

Filomat

View full text Add to dashboard Cite

Due to their applications in many branches of science, topological graph indices are becoming more popular every day. Especially as one can model chemical molecules by graphs to obtain valuable information about the molecules using solely mathematical calculations on the graph. The inverse problem for topological graph indices is a recent problem proposed by Gutman and is about the existence of a graph having its index value equal to a given non-negative integer. In this paper, the inverse problem for Bell index which is one of the irregularity indices is solved. Also a recently defined graph invariant called omega invariant is used to obtain several properties related to the Bell index.

show abstract

“…For a realizable degree sequence D, a new graph invariant called Ω invariant has been introduced in [2]. We briefly recall some fundamental properties of it, see [2,3]…”

Section: ω Invariantmentioning

confidence: 99%

“…In this paper, we shall use some special graph classes of order one, two, three or four. The former two were already used in [3] in solving the extremal problem of finding the maximum number of components amongst all realizations of a given degree sequence. L q is constructed by adding q loops to a single vertex.…”

Section: ω Invariantmentioning

confidence: 99%

Tribonacci graphs

Demırcı

Cangül

2020

ITM Web Conf.

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Extremal Problems on Components and Loops in Graphs

Cited by 14 publications

References 9 publications

Üçgensel sayılar ve graflar

Üçgensel sayılar ve graflar

Inverse problem for Bell index

Tribonacci graphs

Contact Info

Product

Resources

About