At this page we introduce some terminology.

- First we explain the definition
of a 'triangle free strongly regular graph':

- Triangle free means that there is no cycle of length 3 in the graph.

- The degree of a vertex is the number of graph edges which touch the vertex.

- A regular graph is a graph in which every vertex has the same degree.

- A regular graph $G$ is strongly regular if there exist integers $\&lambda,\; \&mu$ so that every pair of adjacent vertices have exactly $\&lambda$ common neighbors, and every pair of nonadjacent vertices have exactly $\&mu$ common neighbors.

To eliminate degeneracies, we shall further assume that $\&mu\; \&ge\; 1$. If $G$ is $k$-regular and the number of vertices $|V(G)|\; =\; n$, then we say that $G$ is a $(n,k,\&lambda,\&mu)$ strongly regular graph.

A useful remark is that triangle free means nothing more than $\&lambda\; =\; 0$

- Triangle free means that there is no cycle of length 3 in the graph.
- Some other definitions:

- The diameter of a graph is the length of the "longest shortest path" between any two graph vertices of a graph.

- The girth is the length of the shortest cycle in a graph (if no cycle exist, the girth is not defined). Remark: triangle free is equivalent with the restriction 'girth > 3'.

- A clique in an (undirected) graph is a subset of its vertices such that every two vertices in the subset are connected by an edge (source: Wikipedia).

- The diameter of a graph is the length of the "longest shortest path" between any two graph vertices of a graph.
- Also a few definitions about Moore graphs:

- A Moore graph is a regular graph of degree d and diameter k whose number of vertices equals the upper bound 1+d\sum_{i=0}^{k-1}(d-1)^i .

An equivalent definition of a Moore graph is that it is a graph of diameter k with girth 2k + 1.

- A Moore graph of type (v,g) is a regular graph of vertex degree v>2 and girth g that contains the maximum possible number of nodes, namely:

_{(g-4)/2}1 + (v-1) ^{(g/2-1)}+ v&sum (v-1) ^{r }for g even, ^{r=0}n(v,g) = _{(g-3)/2}1 + v &sum (v-1) ^{r}for g odd. ^{r=0}

- A Moore graph is a regular graph of degree d and diameter k whose number of vertices equals the upper bound 1+d\sum_{i=0}^{k-1}(d-1)^i .
- About distance-regular and strongly regular graph:

- A connected graph G is distance-regular if for any vertices x and y of G and any integers i, j=0, 1, ... d (where d is the graph diameter), the number of vertices at distance i from x and distance j from y depends only on i, j, and the graph distance between x and y, independently of the choice of x and y.

- In particular, a distance-regular graph is a graph for which there exist integers b
_{i}, c_{i}, i=0,...,d such that for any two vertices x,y in G and distance i=d(x,y), there are exactly c_{i}neighbors of y in G_{(i-1)}(x) and b_{i}neighbors of y in G_{(i+1)}(x), where G_{i}(x) is the set of vertices y of G with d(x,y)=i (Brouwer et al. 1989, p. 434). The array of integers characterizing a distance-regular graph is known as its intersection array.

- A regular graph G is strongly regular if there exist integers $\&lambda,\; \&mu$ so that every pair of adjacent vertices have exactly $\&lambda$ common neighbors, and every pair of nonadjacent vertices have exactly &mu common neighbors.

To eliminate degeneracies, we shall further assume that &mu &ge 1. If G is k-regular and the number of vertices |V(G)| = n, then we say thatG is a (n,k,&lambda,&mu) strongly regular graph.

- A connected graph G is distance-regular if for any vertices x and y of G and any integers i, j=0, 1, ... d (where d is the graph diameter), the number of vertices at distance i from x and distance j from y depends only on i, j, and the graph distance between x and y, independently of the choice of x and y.