Is complete graph strongly regular?
any two adjacent vertices have exactly λ common neighbours; • any two nonadjacent vertices have exactly µ common neighbours. So the Petersen graph is a srg(10,3,0,1). The complete and null graphs are vacuously strongly regular, the param- eters µ and λ respectively being undefined for them.
How many strongly regular graphs are there?
seven
, there are exactly seven known connected triangle-free strongly regular graphs, as summarized in the following table (Godsil 1995) and six of which are illustrated above.
What is a 4 regular graph?
A quartic graph is a graph which is 4-regular. The unique quartic graph on five nodes is the complete graph , and the unique quartic graph on six nodes is the octahedral graph.
How do you find the full size of a graph?
Order of a graph is the number of vertices in the graph. Size of a graph is the number of edges in the graph.
What is regular graph in discrete mathematics?
In graph theory, a regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree or valency. A regular directed graph must also satisfy the stronger condition that the indegree and outdegree of each vertex are equal to each other.
What is a 3 regular graph?
A 3-regular graph is known as a cubic graph. A strongly regular graph is a regular graph where every adjacent pair of vertices has the same number l of neighbors in common, and every non-adjacent pair of vertices has the same number n of neighbors in common.
What is a 2 regular graph?
A two-regular graph is a regular graph for which all local degrees are 2. A two-regular graph consists of one or more (disconnected) cycles.
What is the diameter of a graph?
is a graph distance. In other words, a graph’s diameter is the largest number of vertices which must be traversed in order to travel from one vertex to another when paths which backtrack, detour, or loop are excluded from consideration.
What is a width in a graph?
The width of a graph is an alternative name for the degeneracy of the graph – the smallest k for which every subgraph has degree at most k. Bandwidth of a graph – the minimum, over all orderings of vertices of G, of the length of the longest edge (the number of steps in the ordering between its two endpoints).
What is K6 graph?
The complete graph K6 has 15 edges and 45 pairs of independent edges. It is known that K6 only has good drawings for i independent crossings if and only if either 3 ≤ i ≤ 12 or i = 15; see (Rafla, 1988). Figure 4 gives examples of such good drawings.
What is the odd girth and even girth of a graph?
The odd girth and even girth of a graph are the lengths of a shortest odd cycle and shortest even cycle respectively. The circumference of a graph is the length of the longest (simple) cycle, rather than the shortest.
What graph has a girth of 4?
For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3. A graph with girth four or more is triangle-free .
What is the girth of an undirected graph?
In graph theory, the girth of an undirected graph is the length of a shortest cycle contained in the graph. If the graph does not contain any cycles (that is, it is a forest ), its girth is defined to be infinity. For example, a 4-cycle (square) has girth 4. A grid has girth 4 as well, and a triangular mesh has girth 3.
What is a strongly regular graph with diameter 2?
A strongly regular graph is a distance-regular graph with diameter 2 whenever μ is non-zero. It is a locally linear graph whenever λ = 1 . The four parameters in an srg ( v, k, λ, μ) are not independent and must obey the following relation: