It turns out that this is the only ingredient of the proof where 4‐connectedness is used. Info. A complete digraph is a directed graph in which every pair of distinct vertices is connected by a pair of unique edges (one in each direction). Your Reasoning. About this resource. The motor for our induction is a result of Fontet and Martinov stating that every 4‐connected graph can be reduced to a smaller one by contracting a single edge, unless the graph is the square of a cycle or the line graph of a cubic graph. WARNING: you can only count faces when the graph is drawn in a planar way. LA activity L3. Report a problem. We prove that each {claw, K 4}-free 4-regular graph, with just one class of exceptions, is a line graph.Applying this result, we present lower bounds on the independence numbers for {claw, K 4}-free 4-regular graphs and for {claw, diamond}-free 4-regular graphs.Furthermore, we characterize the extremal graphs attaining the bounds. The number of faces does not change no matter how you draw the graph (as long as you do so without the edges crossing), so it makes sense to ascribe the number of faces as a property of the planar graph. We will just have a horizontal line at #y=4#. They may also be characterized (again with the exception of K 8) as the strongly regular graphs with parameters srg(n(n − 1)/2, 2(n − 2), n − 2, 4). Show all files. rtf, 4 MB. View US version. Record The Order, Size, And Degrees Of The (b) Find The Order, Size, And Vertex Degrees Of L(L(K4)) And L(L(L(K4)). Line Graphs. graph{y=0x+4 [-9.96, 10.04, -3.08, 6.92]} Hope this helps! Updated: Nov 1, 2014. docx, 147 KB. Created: Jun 22, 2014. (a) Draw K4 And The Line Graph L(K4). This implies an affirmative answer to a question of W. Kuehnel whether every 4-connected graph G contains a subdivision H of K4 as a subgraph such that G-V(H) is connected. The line graph of the complete graph K n is also known as the triangular graph, the Johnson graph J(n, 2), or the complement of the Kneser graph KG n,2.Triangular graphs are characterized by their spectra, except for n = 8. doc, 442 KB. Explain (c) 0 Let Lk (G) Be The Graph Obtained By Taking The Line Graph K Times. Uniform Acceleration in One Dimension: Motion Graphs Description This simulation is intended to help anyone get a better understanding of the relationships between various quantities involved in uniformly accelerated motion. (Note: You Do Not Have To Draw The Full Graphs! This resource is designed for UK teachers. HA L5.L6. Mathematics; Mathematics / Data and statistics / Data representation ; 7-11; View more. Categories & Ages. In the mathematical field of graph theory, a complete graph is a simple undirected graph in which every pair of distinct vertices is connected by a unique edge. The only kind of line with a slope of zero is a horizontal line- the only values this equation takes on is when #y=4#; it doesn't matter what #x# is. MA level 4 line graph. So Lo(G)- Vertices. The graph above has 3 faces (yes, we do include the “outside” region as a face). MA level 4 line graph.