On the maximum number of independent edges in cubic graphs

on the number of maximum independent sets of graphs

let $g$ be a simple graph. an independent set is a set ofpairwise non-adjacent vertices. the number of vertices in a maximum independent set of $g$ isdenoted by $alpha(g)$. in this paper, we characterize graphs $g$ with $n$ vertices and with maximumnumber of maximum independent sets provided that $alpha(g)leq 2$ or $alpha(g)geq n-3$.

The Maximum Number of Edges in a Strongly Multiplicative Graph

On the maximum number of edges in quasi-planar graphs

A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a simple proof for this fact that yields the better upper bound of 8n edges for n vertices. Our best construction with 7n−O(1) edges comes very close to this bound. Moreover, we show matching upper and lower bounds for seve...

On the number of maximum independent sets in Doob graphs

The Doob graph D(m,n) is a distance-regular graph with the same parameters as the Hamming graph H(2m+n, 4). The maximum independent sets in the Doob graphs are analogs of the distance-2 MDS codes in the Hamming graphs. We prove that the logarithm of the number of the maximum independent sets in D(m,n) grows as 2(1+o(1)). The main tool for the upper estimation is constructing an injective map fr...

the maximum number of edges in a strongly multiplicative graph

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