Related Experiment Video
Updated: Jul 27, 2025
Microstate and Omega Complexity Analyses of the Resting-state Electroencephalography
Published on: June 15, 2018
New Relations Between Zagreb Indices and Omega Invariant
1Department of Mathematics, Faculty of Arts and Science, Bursa Uludag University, Gorukle Campus, 16059, Bursa - Turkey.
Introduction:
In this work, we studied the problem of determining the values of the Zagreb indices of all the realizations of a given degree sequence.
Method:
We first obtained some new relations between the first and second Zagreb indices and the forgotten index sometimes called the third Zagreb index. These relations also include the triangular numbers, order, size, and the biggest vertex degree of a given graph. As the first Zagreb index and the forgotten index of all the realizations of a given degree sequence are fixed, we concentrated on the values of the second Zagreb index and studied several properties including the effect of vertex addition.
Result:
In our calculations, we make use of a new graph invariant, called omega invariant, to reach numerical and topological values claimed in the theorems. This invariant is closely related to Euler characteristic and the cyclomatic number of graphs.
Conclusion:
Therefore this invariant is used in the calculation of some parameters of the molecular structure under review in terms of vertex degrees, eccentricity, and distance.
Related Concept Videos
01:05Relating Angular And Linear Quantities - II
01:09Relating Angular And Linear Quantities - I
When comparing the linear and rotational variables individually, the linear variable of position has physical units of meters, whereas the angular position variable has dimensionless units of radians, as it is the ratio of two lengths. The linear velocity...
01:24Inertia Tensor
The diagonal components of the inertia tensor matrix represent the moments of inertia concerning the principal axes of the object. These primary axes are defined as the axes where the object experiences the least...
01:15Routh-Hurwitz Criterion I
To apply the Routh-Hurwitz criterion, a Routh table is constructed. The table's rows are labeled with powers of the complex frequency variable s, starting from the...
01:20Moment of Inertia about an Arbitrary Axis
In this scenario, the perpendicular distance between the chosen arbitrary axis...
01:19Routh-Hurwitz Criterion II
The first scenario occurs when a singular zero appears in the first column of the Routh table. This situation creates a division by zero issues. To resolve this, a small positive or negative number, denoted as epsilon (∈), is substituted for the zero. The stability analysis proceeds by assuming a sign for ∈. If ∈ is positive, any sign change in the first...