The first and second Zagreb coindices are defined as respectively. The oldest degree-based topological indices are the first and second Zagreb indices being considered in. Until today, many topology indices have been defined and used as a tool in QSAR/QSPR studies. These constant numbers are used in the modeling of molecules in chemistry and biology. Topological indices are constant numbers that reveal the structure of the graph. For this, topological indices are among the most used tools. The basic idea here is to reveal the properties of molecules using the information corresponding to chemical graphics. Ĭhemical graph theory is the field of study of mathematical chemistry in relation to chemical graphs. For other undefined notations and terminology from graph theory, the readers are referred to. The number of edges of the graph is denoted by, where. Here, any two vertices and are adjacent if and only if they are not adjacent in. The complement of a graph, denoted by, is the graph with the same vertex set. The degree of a vertex in, denoted by, is defined as the number of incident edges to it. Let be a simple graph with a vertex set and edge set, where and. Later, we present precise results for the sigma coindices of various graph operations such as tensor product, Cartesian product, lexicographic product, disjunction, strong product, union, join, and corona product. In this paper, we propose some mathematical properties of the sigma coindex.

The sigma coindex is defined as the sum of the squares of the differences between the degrees of all nonadjacent vertex pairs. Those results should be useful in networks with large degree sequences and cryptographic applications with special numbers. In this work, we determined all the tribonacci graphs of any order by means of some combinatorial results. 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. 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. A graph having a degree sequence consisting of t successive tribonacci numbers is called a tribonacci graph of order t. There is almost no result on the connections between these numbers and graphs. In this paper, we use a generalization of Fibonacci numbers called tribonacci numbers having very limited properties and relations compared to Fibonacci numbers.

Probably the most important of those is the Fibonacci numbers. Special numbers have very important mathematical properties alongside their numerous applications in many ﬁelds of science.

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