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on each partition. The smallest has 110 vertices. The others have 126, 182, 506 and 990. The 126-vertex
Iofinova–Ivanov graph is also known as the
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of the 110-vertex Iofina-Ivanov graph is 2: its vertices can be 2-colored so that no two vertices of the same color are joined by an edge. Its
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Iofinova and Ivanov proved in 1985 the existence of five and only five semi-symmetric cubic bipartite graphs whose automorphism groups act
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with 112. It is only for the five Iofina-Ivanov graphs that the symmetry group acts primitively on each partition of the vertices.
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of the 110-vertex
Iofinova–Ivanov graph, the greatest distance between any pair of vertices, is 7. Its radius is likewise 7. Its
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Few graphs show semi-symmetry: most edge-transitive graphs are also vertex-transitive. The smallest semi-symmetric graph is the
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and 3-edge-connected: to make it disconnected at least three edges, or at least three vertices, must be removed.
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586:. pp. 123–134, 2002. (Vsesoyuz. Nauchno-Issled. Inst. Sistem. Issled., Moscow, pp. 137–152, 1985.)
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608:(Ed. C. J. Colbourn and R. Mathon). Amsterdam, Netherlands: North-Holland, pp. 273–285, 1987.
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394:, with 20 vertices, which is 4-regular. The three smallest cubic semi-symmetric graphs are the
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546:; Potočnik, Primož (2006), "A census of semisymmetric cubic graphs on up to 768 vertices",
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is 3: its edges can be 3-colored so that no two edges of the same color met at a vertex.
528:, vol. 40, no. 845, Ljubljana: Institute of Mathematics, Physics and Mechanics
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398:, with 54 vertices, this the smallest of the Iofina-Ivanov graphs with 110, and the
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Computation of
Lengths of Orbits of a Subgroup in a Transitive Permutation Group.
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367:{\displaystyle (x-3)x^{20}(x+3)(x^{4}-8x^{2}+11)^{12}(x^{4}-6x^{2}+6)^{10}}
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Investigations in the
Algebraic Theory of Combinatorial Objects
374:. The symmetry group of the 110-vertex Iofina-Ivanov is the
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Investigations in
Algebraic Theory of Combinatorial Objects
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Semi-symmetric cubic graph with 110 vertices and 165 edges
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421:"Affine primitive groups and Semisymmetric graphs"
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602:On Edge But Not Vertex Transitive Regular Graphs.
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227:of the 110-vertex Iofina-Ivanov graph is
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597:. Moscow: VNIISI, pp. 3–7, 1983.
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595:Methods for Complex System Studies
578:Iofinova, M. E. and Ivanov, A. A.
548:Journal of Algebraic Combinatorics
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165:with 110 vertices and 165 edges.
152:110-vertex Iofinova–Ivanov graph
22:110-vertex Iofinova–Ivanov graph
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143:Table of graphs and parameters
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472:Iofinova and Ivanov (2013).
606:Combinatorial Design Theory
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580:Bi-Primitive Cubic Graphs.
382:(11), with 1320 elements.
561:10.1007/s10801-006-7397-3
478:. Springer. p. 470.
225:characteristic polynomial
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447:"Iofinova-Ivanov Graphs"
517:; Potočnik, P. (2002),
376:projective linear group
542:; Malnič, Aleksander;
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519:"The Ljubljana Graph"
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219:Algebraic properties
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622:Individual graphs
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445:Weisstein, Eric.
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511:Marušič, D.
197:3-connected
175:primitively
163:cubic graph
136:Hamiltonian
616:Categories
507:Conder, M.
406:References
396:Gray graph
169:Properties
120:Properties
491:12 August
457:11 August
453:. Wolfram
430:12 August
333:−
288:−
241:−
128:bipartite
91:1320 (PGL
203:Coloring
186:diameter
67:Diameter
37:Vertices
192:is 10.
154:is, in
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195:It is
57:Radius
522:(PDF)
190:girth
132:cubic
95:(11))
77:Girth
47:Edges
493:2015
480:ISBN
459:2015
432:2015
223:The
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378:PGL
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