The Lower Bipartite Number of a Graph

Uniform Number of a Graph

We introduce the notion of uniform number of a graph. The  uniform number of a connected graph $G$ is the least cardinality of a nonempty subset $M$ of the vertex set of $G$ for which the function $f_M: M^crightarrow mathcal{P}(X) - {emptyset}$ defined as $f_M(x) = {D(x, y): y in M}$ is a constant function, where $D(x, y)$ is the detour distance between $x$ and $y$ in $G$ and $mathcal{P}(X)$ ...

On the number of maximal bipartite subgraphs of a graph

We show new lower and upper bounds on the number of maximal induced bipartite subgraphs of graphs with n vertices. We present an infinite family of graphs having 105n/10 ≈ 1.5926n such subgraphs, which improves an earlier lower bound by Schiermeyer (1996). We show an upper bound of n·12n/4 ≈ n·1.8613n and give an algorithm that lists all maximal induced bipartite subgraphs in time proportional ...

The convex domination subdivision number of a graph

Let $G=(V,E)$ be a simple graph. A set $Dsubseteq V$ is adominating set of $G$ if every vertex in $Vsetminus D$ has atleast one neighbor in $D$. The distance $d_G(u,v)$ between twovertices $u$ and $v$ is the length of a shortest $(u,v)$-path in$G$. An $(u,v)$-path of length $d_G(u,v)$ is called an$(u,v)$-geodesic. A set $Xsubseteq V$ is convex in $G$ ifvertices from all $(a, b)$-geodesics belon...

The relationship between the distinguishing number and the distinguishing index with detection number of a graph

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The Maximum Number of Edges in a Strongly Multiplicative Graph