Connected simple graphs and a selection problem

A simple linear algorithm for the connected domination problem in circular-arc graphs

A connected dominating set of a graph G = (V, E) is a subset of vertices CD ⊆ V such that every vertex not in CD is adjacent to at least one vertex in CD, and the subgraph induced by CD is connected. We show that, given an arc family F with endpoints sorted, a minimum-cardinality connected dominating set of the circular-arc graph constructed from F can be computed in O(|F |) time.

a simple approach to order the multiplicative zagreb indices of connected graphs

the first ($pi_1$) and the second $(pi_2$) multiplicative zagreb indices of a connected graph $g$, with vertex set $v(g)$ and edge set $e(g)$, are defined as $pi_1(g) = prod_{u in v(g)} {d_u}^2$ and $pi_2(g) = prod_{uv in e(g)} {d_u}d_{v}$, respectively, where ${d_u}$ denotes the degree of the vertex $u$. in this paper we present a simple approach to order these indices for connected graphs on ...

A cycle embedding problem for Cube-Connected Cycles Graphs

Let n be an odd integer with n ≥ 3. The cube-connected cycles graph CCCn has n × 2 vertices, labeled (l,x), where 0 ≤ l ≤ n − 1 and x is an n-bit binary string. Two vertices (l,x) and (l′,y) are adjacent if and only if either x = y and |l − l′| = 1, or l = l′ and y = (x). In this paper, we will find the set of all possible lengths of cycles in CCCn with n is odd and n ≥ 3 .

connected graphs cospectral with a friendship graph

let $n$ be any positive integer, the friendship graph $f_n$ consists of $n$ edge-disjoint triangles that all of them meeting in one vertex. a graph $g$ is called cospectral with a graph $h$ if their adjacency matrices have the same eigenvalues. recently in href{http://arxiv.org/pdf/1310.6529v1.pdf}{http://arxiv.org/pdf/1310.6529v1.pdf} it is proved that if $g$ is any graph cospectral with $f_n$...

The Simple Reachability Problem in Switch Graphs