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In this paper we consider a fundamental problem in the area of viralmarketing, called T{\scriptsize ARGET} S{\scriptsize ET} S{\scriptsizeELECTION} problem.  In a a viral marketing setting, social networks are modeled by graphs withpotential customers of a new product as vertices and friend relationships asedges, where each vertex $v$ is assigned a threshold value $\theta(v)$. Thethresholds represent the different latent tendencies of customers (vertices) tobuy the new product when their friend (neighbors) do.  Consider a repetitive process on social network $(G,\theta)$ where eachvertex $v$ is associated with two states, active and inactive, which indicatewhether $v$ is persuaded into buying the new product. Suppose we are given atarget set $S\subseteq V(G)$. Initially, all vertices in $G$ are inactive. Attime step 0, we choose all vertices in $S$ to become active.  Then, at every time step $t>0$, all vertices that were active in time step$t-1$ remain active, and we activate any vertex $v$ if at least $\theta(v)$ ofits neighbors were active at time step $t-1$. The activation process terminateswhen no more vertices can get activated. We are interested in the followingoptimization problem, called T{\scriptsize ARGET} S{\scriptsize ET}S{\scriptsize ELECTION}: Finding a target set $S$ of smallest possible sizethat activates all vertices of $G$. There is an important and well-studiedthreshold called strict majority threshold, where for every vertex $v$ in $G$we have $\theta(v)=\lceil{(d(v) +1)/2}\rceil$ and $d(v)$ is the degree of $v$in $G$. In this paper, we consider the T{\scriptsize ARGET} S{\scriptsize ET}S{\scriptsize ELECTION} problem under strict majority thresholds and focus onthree popular regular network structures: cycle permutation graphs, generalizedPetersen graphs and torus cordalis.

The Target Set Selection Problem on Cycle Permutation Graphs, Generalized Petersen Graphs and Torus Cordalis