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Conference graph

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The eigenvalues of a conference graph need not be integers, unlike those of other strongly regular graphs. If the graph is connected, the eigenvalues are
32: 345: 289: 281: 374: 364: 90: 62: 47: 69: 379: 208: 173: 76: 338: 58: 369: 127: 331: 169: 285: 277: 161: 83: 315: 269: 358: 191:) for all prime powers congruent to 1 (modulo 4). However, there are many values of 311: 119: 188: 115: 21: 195:
that are allowed, for which the existence of a conference graph is unknown.
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Conference graphs are known to exist for all small values of
319: 43: 211: 242: 202:with multiplicity 1, and two other eigenvalues, 243:{\displaystyle {\frac {-1\pm {\sqrt {v}}}{2}},} 339: 8: 160:It is the graph associated with a symmetric 48:introducing citations to additional sources 346: 332: 224: 212: 210: 272:, Cohen, A.M., and Neumaier, A. (1989), 111:Special case of a strongly regular graph 38:Relevant discussion may be found on the 276:. Berlin, New York: Springer-Verlag. 7: 300: 298: 183:allowed by the restrictions, e.g., 318:. You can help Knowledge (XXG) by 14: 187:= 5, 9, 13, 17, 25, 29, and (the 302: 31:relies largely or entirely on a 20: 1: 164:, and consequently its order 396: 297: 375:Strongly regular graphs 274:Distance Regular Graphs 253:each with multiplicity 365:Algebraic graph theory 314:-related article is a 244: 128:strongly regular graph 245: 209: 44:improve this article 380:Graph theory stubs 240: 174:sum of two squares 59:"Conference graph" 327: 326: 235: 229: 162:conference matrix 109: 108: 94: 387: 348: 341: 334: 306: 299: 275: 260: 249: 247: 246: 241: 236: 231: 230: 225: 213: 159: 151: 144: 130:with parameters 124:conference graph 104: 101: 95: 93: 52: 24: 16: 395: 394: 390: 389: 388: 386: 385: 384: 355: 354: 353: 352: 295: 273: 266: 254: 214: 207: 206: 153: 145: 135: 112: 105: 99: 96: 53: 51: 37: 25: 12: 11: 5: 393: 391: 383: 382: 377: 372: 370:Graph families 367: 357: 356: 351: 350: 343: 336: 328: 325: 324: 307: 293: 292: 265: 262: 251: 250: 239: 234: 228: 223: 220: 217: 110: 107: 106: 42:. Please help 28: 26: 19: 13: 10: 9: 6: 4: 3: 2: 392: 381: 378: 376: 373: 371: 368: 366: 363: 362: 360: 349: 344: 342: 337: 335: 330: 329: 323: 321: 317: 313: 308: 305: 301: 296: 291: 290:0-387-50619-5 287: 283: 282:3-540-50619-5 279: 271: 270:Brouwer, A.E. 268: 267: 263: 261: 259:− 1)/2. 258: 237: 232: 226: 221: 218: 215: 205: 204: 203: 201: 196: 194: 190: 186: 182: 177: 175: 171: 167: 163: 158:− 1)/4. 157: 150:− 5)/4, 149: 143:− 1)/2, 142: 138: 133: 129: 125: 121: 117: 103: 92: 89: 85: 82: 78: 75: 71: 68: 64: 61: –  60: 56: 55:Find sources: 49: 45: 41: 35: 34: 33:single source 29:This article 27: 23: 18: 17: 320:expanding it 312:graph theory 309: 294: 256: 252: 199: 197: 192: 189:Paley graphs 184: 180: 178: 165: 155: 147: 140: 136: 131: 123: 120:graph theory 116:mathematical 113: 97: 87: 80: 73: 66: 54: 30: 168:must be 1 ( 359:Categories 264:References 100:April 2024 70:newspapers 222:± 216:− 172:4) and a 40:talk page 118:area of 114:In the 84:scholar 288:  280:  170:modulo 86:  79:  72:  65:  57:  310:This 154:μ = ( 146:λ = ( 126:is a 91:JSTOR 77:books 316:stub 286:ISBN 278:ISBN 152:and 122:, a 63:news 139:= ( 46:by 361:: 284:, 176:. 134:, 347:e 340:t 333:v 322:. 257:v 255:( 238:, 233:2 227:v 219:1 200:k 193:v 185:v 181:v 166:v 156:v 148:v 141:v 137:k 132:v 102:) 98:( 88:· 81:· 74:· 67:· 50:. 36:.

Index


single source
talk page
improve this article
introducing citations to additional sources
"Conference graph"
news
newspapers
books
scholar
JSTOR
mathematical
graph theory
strongly regular graph
conference matrix
modulo
sum of two squares
Paley graphs
Brouwer, A.E.
ISBN
3-540-50619-5
ISBN
0-387-50619-5
Stub icon
graph theory
stub
expanding it
v
t
e

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