Sentence examples for total graphs from inspiring English sources

We finally consider the case of total graphs.

Gao et al. [15] established formulas and lower bounds of the Kirchhoff index of line, subdivision and total graphs of a regular graph.

We defined molecule type graphs (19 total graphs) to represent molecules (18 proteins and phosphatidylinositol) and rules (544) to represent molecular interactions and other processes (viz. transport and degradation).

In this paper we first prove that a connected graph is a tree if and only if its total graph is strongly chordal, and thus we obtain a polynomial-time algorithm for this problem in trees.

The graph (T(G)) is called the total graph of G.  .

In this section, we investigate IE of line graph, subdivision graph, para-line graph and total graph of a regular graph.

In this section, we consider LEL of line graph, subdivision graph, para-line graph, and total graph of a regular graph.

The line graph, subdivision graph, para-line graph and total graph are the well-known operations on graphs, which can produce many new types of graphs.

In this paper, we present some new upper and lower bounds on LEL and IE of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve previously known results.

Recently, in [17], Wang and Luo presented upper and lower bounds for the Laplaican-energy-like invariant of line graph, subdivision graph and total graph of a regular graph.

In this paper, we give some new upper and lower bounds on the Laplacian-energy-like invariant and the incidence energy of line graph, subdivision graph, para-line graph and total graph of a regular graph, some of which improve the corresponding bounds in [17] and [12].