# 1/2-Transitive Graphs of Order 3p by Alspach B., Xu M.Y.

By Alspach B., Xu M.Y.

**Read or Download 1/2-Transitive Graphs of Order 3p PDF**

**Similar graph theory books**

Protecting a variety of Random Graphs matters, this quantity examines series-parallel networks, houses of random subgraphs of the n-cube, random binary and recursive timber, random digraphs, precipitated subgraphs and spanning bushes in random graphs in addition to matchings, hamiltonian cycles and closure in such buildings.

**Bayesian Networks and Decision Graphs**

Probabilistic graphical types and selection graphs are robust modeling instruments for reasoning and choice making less than uncertainty. As modeling languages they enable a average specification of challenge domain names with inherent uncertainty, and from a computational standpoint they help effective algorithms for automated development and question answering.

**Graph Colouring and the Probabilistic Method**

Over the last decade, many significant advances were made within the box of graph coloring through the probabilistic procedure. This monograph, through of the easiest at the subject, offers an obtainable and unified therapy of those effects, utilizing instruments corresponding to the Lovasz neighborhood Lemma and Talagrand's focus inequality.

**An Introduction to Catalan Numbers**

This textbook presents an advent to the Catalan numbers and their striking homes, in addition to their a number of functions in combinatorics. Intended to be obtainable to scholars new to the topic, the ebook starts with extra trouble-free themes ahead of progressing to extra mathematically subtle themes.

- Looking at Numbers
- Graphs and Cubes (Universitext)
- Graph Theory with Applications to Engineering and Computer Science (Dover Books on Mathematics)
- Graph drawing and applications 1, Edition: 1st

**Extra resources for 1/2-Transitive Graphs of Order 3p**

**Example text**

8. EULERIAN GRAPHS theorern is true for n = 1 clearly. Suppose n 2:: 2 and the theorern holds for any two vertices of B (d, n - 1). Assurne that x and y are two distinct vertices of B(d, n). First, we consider the case that (x, y) is not an edge of B(d, n). Since B(d,n) = L(B(d,n- 1)), x and y correspond to two edges in B(d,n- 1). Let such two edges be x = (u,u') and y = (v,v'). Then u' -1- v since (x,y) is not an edge of B(d, n). By induction hypothesis, there are d- 1 internally disjoint (u',v)-paths of length at rnost n in B(d,n -1), frorn which we can induce d - l internally disjoint (x, y)-paths of length at rnost n+ 1 in B(d, n).

Example 1. 1 Let G be an undirected graph with J 2:: 2. Then G contains a cycle certainly. Moreover, if G is simple, then G contains a cycle of length at least J + 1. Proof If G contains loops or parallel edges, then the conclusion holds clearly. Suppose that G is simple below and let P = (x 0 , x 1 , · · ·, xk) be a Iongest path in G. Then all neighbors of x 0 must lie on P, that is Note that \Na(xo)\ = dc(xo) 2:: J(G) = J 2:: 2. Thus, there exists Xi E Na(xo), J ~ i ~ k. It follows that (xo,xl, · · · ,Xi-l, 1 Xi, xo) is a cycle of length at least J + 1 in G.

5 Prove that the cartesian product of two eulerian graphs is an eulerian graph, hence 2n-cube Q2n is an eulerian graph. 6 (a) Prove that if Gis a connected digraph, ld(t(x)- da(x)l ~ 1 for any x E V and any edge of G is not contained in odd number of directed cycles, then G is eulerian. (b) Give an example to show that the converse of (a) is not true. 8. 7 Prove that a connected undirected G is eulerian if and only if every edge of G lies on an odd number of cycles. 8 Let G be an eulerian graph and x be a vertex of G.