It is clear from x-axis that a few nodes are having a minimum degree and lie near the origin on the x-axis.
Again, there is a negative correlation between the rank difference and the minimum degree and average degree (Fig. S2), which shows that KI is also able to predict interactions for proteins with few training examples.
In this section, by considering the graph Γ ( S M ) defined as in the first section, we will mainly deal with the graph properties, namely diameter, girth, maximum and minimum degrees, domination number and finally irregularity index of it.
Then in Section 2, we compute the diameter, maximum and minimum degrees, girth, chromatic, clique and domination numbers, degree sequence and finally irregularity index of graphs Γ ( G i ) for each 1 ≤ i ≤ 5. Remark 1 The reason for us to present our results on these above parameters actually comes from their equality status.
In this paper, firstly, we define a new graph based on the semi-direct product of a free abelian monoid of rank n by a finite cyclic monoid, and then discuss some graph properties on this new graph, namely diameter, maximum and minimum degrees, girth, degree sequence and irregularity index, domination number, chromatic number, clique number of Γ ( P M ).
The maximum and minimum degrees of G are denoted by Δ and δ, respectively.
In fact, by the graph-theoretic properties, we will be interested in the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of the corresponding new graph.
In this section, by considering the graph Γ ( G i ), 1 ≤ i ≤ 5, we mainly deal with some graph properties, namely diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of Γ ( G i ).
By group-theoretic property, while we deal with the Gröbner-Shirshov basis of a given group, by graph-theoretic property, we are interested in the diameter, maximum and minimum degrees, girth, chromatic number, clique number, domination number, degree sequence and irregularity index of the corresponding graph of group.
In this section, by considering the graph Γ ( P M ) drawn in Figure 1, we mainly deal with some graph properties, namely diameter, maximum and minimum degrees, girth, degree sequence, irregularity index, domination number, chromatic number and clique number of Γ ( P M ).
