Extremal graphs of order dimension 4

Extremal Graphs of Order Dimension 4

We will examine the maximal number of edges of a graph on p vertices of order dimension 4. We will show that the lower bound for this number is greater than 3 8 p 2 + 2p − 13. In particular the Turán-4 graph on p vertices does not have the maximal number of edges among the graphs of order dimension 4.

Extremal graphs without 4-cycles

We prove an upper bound for the number of edges a C4-free graph on q 2 + q vertices can contain for q even. This upper bound is achieved whenever there is an orthogonal polarity graph of a plane of even order q. Let n be a positive integer and G a graph. We define ex(n,G) to be the largest number of edges possible in a graph on n vertices that does not contain G as a subgraph; we call a graph o...

Extremal Sets Minimizing Dimension-normalized Boundary in Hamming Graphs∗

We prove that the set of first k vertices of a Hamming graph in reverse-lexicographic order constitutes an extremal set minimizing the dimension-normalized edge-boundary over all kvertex subsets of the graph. This generalizes a result of Lindsey and can be used to prove a tight lower bound for the isoperimetric number and the bisection width of arrays.

Extremal Sets Minimizing Dimension-Normalized Boundary in Hamming Graphs

Eccentric Connectivity Index: Extremal Graphs and Values

Eccentric connectivity index has been found to have a low degeneracy and hence a significant potential of predicting biological activity of certain classes of chemical compounds. We present here explicit formulas for eccentric connectivity index of various families of graphs. We also show that the eccentric connectivity index grows at most polynomially with the number of vertices and determine ...