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2-Connectedthe property that a graph cannot be disconnected by removing only one vertex

2-Pebbling Propertytwo pebbles can be moved to any specified vertex when the initial configuration $C$ has size $2\pi(G)-s(C)+1$, where $s(C)$ is the size of the support

Bipartite Grapha graph whose vertices can be covered by two sets of pairwise nonadjacent vertices

Bookthe graph $S_{p+1} \times P_q$, having $p$ pages, $q$ vertices per page, and $q$ vertices on the binding.

Cartesian ProductG_{1}x G_{2}has vertex set $V(G_1 \times G_2) = \{(v_1,v_2) | v_1 \in V(G_1), v_2 \in V(G_2) \}$ and edge set $E(G_1 \times G_2) = \{\{(v_1,v_2),(w_1,w_2)\} | (v_1=w_1$ $and$ $(v_2,w_2) \in E(G_2))$ $or$ $(v_2=w_2$ $and$ $(v_1,w_1) \in E(G_1))\}$

Class 0the property that a graph has pebbling number equal to its number of vertices

Completethe property that a graph has every vertex adjacent to all other vertices

Complete Bipartite Grapha bipartite graph in which every pair of vertices not belonging to the same partite set is adjacent

Configurationa function that indicates the number of pebbles per vertex

Connectivitythe minimum number of vertices whose deletion disconnects the graph or reduces it to one vertex

Cover Pebbling Numberthe minimum number of pebbles needed so that from any initial configuration of the pebbles, after a series of pebbling moves, it is possible to have at least $1$ pebble on every vertex of a graph

Cover Pebbling Ratiofor a graph $G$, the cover pebbling number of $G$ divided by the pebbling number of $G$

Cross Numberfor a sequence $S$ in a group, the value: $\displaystyle{\sum_{g \in S}\frac{1}{|g|}}$

Cubea graph that has all binary $d$-tuples as vertices and edges between that differ in exactly one coordinate

Cyclea simple graph whose vertices can be placed on a circle so that vertices are adjacent if and only if they appear consecutively on the circle

Davenport's Constantthe smallest $D$ such that every sequence of $D$ elements contains a zero-sum subsequence

Diameterthe maximum distance between two vertices of a graph

Dominating Seta subset $S$ of the vertex set of a graph such that every vertex outside of $S$ has a neighbor in $S$

Domination Numberthe minimum size of a dominating set of vertices

Fractional Pebbling Number$\liminf_{k \rightarrow \infty} \pi(G)/k$

Fusethe graph on $n$ vertices composed of a path on $l$ vertices with $n-l$ independent vertices incident to one of its endpoints

Girththe length of a shortest cycle in a graph

Greedy Grapha graph $G$ for which every configuration of size $\pi(G)$ has a greedy slolution

Greedy Solutiona pebbling solution in which every step is greedy

Greedy Stepa pebbling step from a vertex $u$ to a vertex $v$ such that ${\rm dist}(v,r)<{\rm dist}(u,r)$, where $r$ is the root vertex

H-Sum Sequencefor a subgroup $H$ of a group $G$, a sequence of elements of $G$ that sums to an element of $H$

Kneser Graphthe graph with vertices ${[m] \choose t}$ and edges $\{A,B\}$ whenever $A$ and $B$ are disjoint

Majorizethe sequence $(s_1,\ldots,s_k)$ majorizes the sequence $(t_1,\ldots,t_k)$ if $s_i > t_i$ when $s_j=t_j$ for all $jMaximum Path Partitiona path partition of a tree $T$ such that no other path partition majorizes itOptimal Pebbling Numberthe size of the smallest solvable configuration in a graphPatha sequence of vertices, each adjacent to its successorPath Partitionan $r$-path partition for some $r$Pebbling Numberthe fewest number of pebbles that gurantee that a specific graph is solvablePebbling Thresholda threshold for the solvability of random pebbling configurations on graph sequencesPetersen Graphthe disjointness graph of the $2$-sets in a $5$-element setPositive Weight Function$w(v)>0$ for every vertex $v$, where $w(v)$ is the number of pebbles on vertex $v$$q$-Pebbling Stepconsists of removing $q$ pebbles from a vertex $u$, and placing one pebble on a neighbor $v$ of $u$$r$-Maximum Path Partitionan $r$-path partition of a tree $T$ such that no other $r$-path partition majorizes it$r$-Path Partitiona partition $Q=(Q_1,\ldots,Q_m)$ of the edges of a tree $T$ into paths such that each path $Q_i$ is well $r$-directedr-Solvablethe property that there is a sequence of pebbling moves for a given graph such that it is possible to place a pebble on the rootr-Unsolvablethe property that for a given graph, it is not possible to place a pebble on the root through a sequence of pebbling movesRootthe pebbling targetSemi-greedya pebbling step from a vertex $u$ to a vertex $v$ such that ${\rm dist}(v,r) \leq {\rm dist}(u,r)$, where $r$ is the root vertexSimple Configurationall pebbles are concentrated on a single vertexSolvablea configuration that is $r$-solvable for every root $r$Stara graph made up of one vertex adjacent to each of $n$ independent verticesSupportthe set of all vertices that have at least one pebbleThresholdfor a property $\mathbf{P}$ of a random structure $S_p$, the set of functions $t$ for which $p \gg t$ implies that $Pr[S_p$ $has$ $\mathbf{P}] \rightarrow 0$ as $n \rightarrow \infty$, and $p \ll t$ implies that $Pr[S_p$ $has$ $\mathbf{P}] \rightarrow 1$ as $n \rightarrow \infty$Treea connected graph with no cyclesTree-Solvablethe property that every configuration of size at least $\pi(G)$ has a solution in which the edges traversed by pebbling steps form an acyclic subgraphWeighted Cover Pebbling Numberthe minimum number of pebbles needed to place, after a sequence of pebbling steps, $w(v)$ pebbles on vertex $v$, for all $v$, regardless of the initial configurationWeighted Pebbling Numberthe minimum number $t$ so that, for every weight function $w$ with $|w|=\mathbf{w}$, every configuration of $t$ pebbles is $w$-solvableWell $r$-DirectedAn orientatiuon of the edges of a path $P$ with one endpoint $r$ for which every edge points to $r$Zero-Sum Sequencea sequence of elements of a finite group $G$ that sums to the identity of $G$