Locally linear graph: Difference between revisions

Revision as of 08:09, 19 February 2019

Revision as of 08:35, 19 February 2019

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The [[Cartesian product of graphs|Cartesian product]] of any two locally linear graphs remains locally linear, because any triangles in the product come from triangles in one or the other factors. For instance, the nine-vertex [[Paley graph]] (the graph of the [[3-3 duoprism]]) is the Cartesian product of two triangles.{{r|f}}

The [[Hamming graph]]s <math>H(d,3)</math> are products of <math>d</math> triangles, and again are locally linear.{{r|djlp}}

===Expansion===

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| volume = 72

| year = 2005}}</ref>

<ref name=djlp>{{citation

| last1 = Devillers | first1 = Alice

| last2 = Jin | first2 = Wei

| last3 = Li | first3 = Cai Heng

| last4 = Praeger | first4 = Cheryl E.

| doi = 10.1016/j.jcta.2012.10.004

| issue = 2

| journal = Journal of Combinatorial Theory

| mr = 2995054

| pages = 500–508

| series = Series A

| title = Local 2-geodesic transitivity and clique graphs

| volume = 120

| year = 2013}}. In the notation of this reference, the family of <math>2r</math>-regular graphs is denoted as <math>F(r,2)</math>.</ref>

<ref name=ers>{{citation