id sid eid entity type cana-4515 1 1 1074 CARDINAL cana-4515 1 2 32 CARDINAL cana-4515 2 1 9s CARDINAL cana-4515 2 2 2290 CARDINAL cana-4515 2 3 iqbal m. batiha1,2 PERSON cana-4515 2 4 batiha3 PERSON cana-4515 3 1 iqbal h. jebril1 PERSON cana-4515 3 2 hamzah o. al-khawaldeh4 PERSON cana-4515 3 3 mohamed5 1department PERSON cana-4515 3 4 al zaytoonah university of jordan ORG cana-4515 3 5 11733 DATE cana-4515 3 6 jordan 2nonlinear ORG cana-4515 3 7 ajman university ORG cana-4515 3 8 346 CARDINAL cana-4515 3 9 united arab NORP cana-4515 4 1 3department CARDINAL cana-4515 4 2 jadara university ORG cana-4515 4 3 jordan 4department PERSON cana-4515 4 4 al al-bayt university PERSON cana-4515 4 5 mafraq GPE cana-4515 4 6 jordan 5giza PERSON cana-4515 4 7 tomah GPE cana-4515 4 8 eygpt article ORG cana-4515 4 9 12-01-2025 CARDINAL cana-4515 4 10 15-02-2025 CARDINAL cana-4515 4 11 01-03-2025 CARDINAL cana-4515 7 1 kirchhoff ORG cana-4515 8 1 dodgson PERSON cana-4515 11 1 1 CARDINAL cana-4515 13 1 three CARDINAL cana-4515 13 2 1 CARDINAL cana-4515 13 3 2 CARDINAL cana-4515 13 4 3-5 CARDINAL cana-4515 14 1 kirchhoff ORG cana-4515 15 1 6 CARDINAL cana-4515 16 1 kirchhoff ORG cana-4515 20 1 βˆ’1 DATE cana-4515 27 1 0 CARDINAL cana-4515 29 1 1/π‘βˆ CARDINAL cana-4515 30 1 1074 CARDINAL cana-4515 30 2 32 CARDINAL cana-4515 31 1 9s CARDINAL cana-4515 31 2 2291 CARDINAL cana-4515 31 3 1/π‘βˆ CARDINAL cana-4515 32 1 πœ†0 CARDINAL cana-4515 34 1 πœ†π‘βˆ’1 LOC cana-4515 36 1 one CARDINAL cana-4515 36 2 first ORDINAL cana-4515 36 3 8 CARDINAL cana-4515 36 4 π‘›π‘›βˆ’2 ORG cana-4515 36 5 π‘›βˆ’2 PRODUCT cana-4515 36 6 2 CARDINAL cana-4515 36 7 bipartite NORP cana-4515 36 8 bipartite ORG cana-4515 38 1 zhang et al PERSON cana-4515 39 1 11 CARDINAL cana-4515 40 1 3 CARDINAL cana-4515 40 2 luo et al PERSON cana-4515 41 1 12 CARDINAL cana-4515 42 1 sotirov et al PERSON cana-4515 43 1 13 CARDINAL cana-4515 44 1 mohamed et al PERSON cana-4515 45 1 14 CARDINAL cana-4515 46 1 daoud PERSON cana-4515 47 1 15 CARDINAL cana-4515 47 2 cartesian NORP cana-4515 49 1 1.1 CARDINAL cana-4515 49 2 n Γ— n ORG cana-4515 49 3 16 CARDINAL cana-4515 49 4 17 CARDINAL cana-4515 50 1 π‘Žπ‘›2 DATE cana-4515 54 1 π‘Ž2𝑛 TIME cana-4515 58 1 π‘Žπ‘›1 π‘Žπ‘›3 PERSON cana-4515 59 1 π‘Ž1𝑛 π‘Žπ‘›1 PERSON cana-4515 61 1 1 CARDINAL cana-4515 61 2 1.2 CARDINAL cana-4515 61 3 2 CARDINAL cana-4515 61 4 dodgson PERSON cana-4515 61 5 n Γ— n ORG cana-4515 61 6 18 CARDINAL cana-4515 62 1 dodgson PERSON cana-4515 62 2 4 CARDINAL cana-4515 62 3 n Γ— n ORG cana-4515 62 4 first ORDINAL cana-4515 62 5 first ORDINAL cana-4515 62 6 first ORDINAL cana-4515 62 7 last row DATE cana-4515 62 8 first ORDINAL cana-4515 62 9 only one CARDINAL cana-4515 62 10 one CARDINAL cana-4515 62 11 n Γ— n ORG cana-4515 62 12 1 CARDINAL cana-4515 62 13 0 CARDINAL cana-4515 62 14 1074 CARDINAL cana-4515 62 15 32 CARDINAL cana-4515 63 1 9s CARDINAL cana-4515 63 2 2292 CARDINAL cana-4515 64 1 1.2.1 CARDINAL cana-4515 64 2 𝐿𝑛π‘₯𝑛 ORG cana-4515 64 3 𝑳 = π‘«βˆ’ 𝑨: PERSON cana-4515 67 1 βˆ’1 DATE cana-4515 68 1 0 CARDINAL cana-4515 68 2 1.2.2 CARDINAL cana-4515 68 3 two CARDINAL cana-4515 69 1 19 CARDINAL cana-4515 70 1 20,21,22,23,24,25,26,27,28,29 CARDINAL cana-4515 71 1 2 CARDINAL cana-4515 71 2 2.1 CARDINAL cana-4515 72 1 2n CARDINAL cana-4515 72 2 2 CARDINAL cana-4515 74 1 100 CARDINAL cana-4515 77 1 1 CARDINAL cana-4515 77 2 1 CARDINAL cana-4515 77 3 2Γ—2 CARDINAL cana-4515 77 4 1 520 CARDINAL cana-4515 77 5 480 CARDINAL cana-4515 77 6 800 CARDINAL cana-4515 78 1 1074 CARDINAL cana-4515 78 2 32 CARDINAL cana-4515 79 1 9s CARDINAL cana-4515 79 2 2025 CARDINAL cana-4515 79 3 2293 DATE cana-4515 80 1 + 1 DATE cana-4515 80 2 dodgson PERSON cana-4515 81 1 2 CARDINAL cana-4515 83 1 2 CARDINAL cana-4515 86 1 0 CARDINAL cana-4515 86 2 0 CARDINAL cana-4515 86 3 0 CARDINAL cana-4515 86 4 0 CARDINAL cana-4515 88 1 0 CARDINAL cana-4515 90 1 2π‘˜+5)Γ—(2π‘˜+5 CARDINAL cana-4515 91 1 1 CARDINAL cana-4515 91 2 15 CARDINAL cana-4515 91 3 8π‘˜ CARDINAL cana-4515 92 1 60 Γ— 8π‘˜ PERCENT cana-4515 92 2 50 Γ— 8π‘˜ PERCENT cana-4515 92 3 150 + DATE cana-4515 92 4 25 CARDINAL cana-4515 95 1 100 CARDINAL cana-4515 98 1 4 CARDINAL cana-4515 100 1 βˆ’1 DATE cana-4515 100 2 0 CARDINAL cana-4515 100 3 βˆ’1 DATE cana-4515 100 4 0 β‹± β‹± β‹± β‹± β‹± β‹± WORK_OF_ART cana-4515 100 5 0 CARDINAL cana-4515 108 1 2 CARDINAL cana-4515 111 1 0 CARDINAL cana-4515 111 2 βˆ’1 DATE cana-4515 111 3 0 CARDINAL cana-4515 111 4 β‹± β‹± WORK_OF_ART cana-4515 111 5 βˆ’1 DATE cana-4515 112 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 115 1 βˆ’1 DATE cana-4515 115 2 βˆ’1 DATE cana-4515 115 3 0 CARDINAL cana-4515 115 4 βˆ’1 CARDINAL cana-4515 115 5 0 CARDINAL cana-4515 115 6 0 CARDINAL cana-4515 115 7 βˆ’1 DATE cana-4515 115 8 βˆ’1 DATE cana-4515 115 9 0 β‹― βˆ’1 4 MONEY cana-4515 116 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 118 1 βˆ’1 DATE cana-4515 118 2 0 CARDINAL cana-4515 118 3 0 CARDINAL cana-4515 118 4 β‹± β‹± WORK_OF_ART cana-4515 118 5 0 CARDINAL cana-4515 118 6 4 CARDINAL cana-4515 118 7 βˆ’1 DATE cana-4515 119 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 121 1 4 CARDINAL cana-4515 123 1 βˆ’1 DATE cana-4515 123 2 βˆ’1 DATE cana-4515 123 3 0 CARDINAL cana-4515 123 4 0 CARDINAL cana-4515 123 5 βˆ’1 DATE cana-4515 123 6 βˆ’1 DATE cana-4515 123 7 0 CARDINAL cana-4515 124 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 127 1 1 𝑆 QUANTITY cana-4515 127 2 1 CARDINAL cana-4515 128 1 4 CARDINAL cana-4515 130 1 βˆ’1 DATE cana-4515 130 2 0 CARDINAL cana-4515 130 3 βˆ’1 DATE cana-4515 130 4 0 β‹± β‹± β‹± β‹± β‹± β‹± WORK_OF_ART cana-4515 130 5 0 CARDINAL cana-4515 131 1 1074 CARDINAL cana-4515 131 2 32 CARDINAL cana-4515 132 1 9s CARDINAL cana-4515 132 2 2025 DATE cana-4515 132 3 2294 CARDINAL cana-4515 133 1 2 CARDINAL cana-4515 136 1 0 CARDINAL cana-4515 136 2 βˆ’1 DATE cana-4515 136 3 0 CARDINAL cana-4515 136 4 β‹± β‹± WORK_OF_ART cana-4515 136 5 βˆ’1 DATE cana-4515 142 1 βˆ’1 DATE cana-4515 142 2 βˆ’1 DATE cana-4515 142 3 0 CARDINAL cana-4515 142 4 βˆ’1 CARDINAL cana-4515 142 5 0 CARDINAL cana-4515 142 6 0 CARDINAL cana-4515 142 7 βˆ’1 DATE cana-4515 142 8 βˆ’1 DATE cana-4515 142 9 0 β‹― βˆ’1 4 MONEY cana-4515 145 1 βˆ’1 DATE cana-4515 145 2 0 CARDINAL cana-4515 145 3 0 CARDINAL cana-4515 145 4 β‹± β‹± WORK_OF_ART cana-4515 145 5 0 CARDINAL cana-4515 145 6 4 CARDINAL cana-4515 145 7 βˆ’1 DATE cana-4515 147 1 4 CARDINAL cana-4515 149 1 βˆ’1 DATE cana-4515 149 2 βˆ’1 DATE cana-4515 149 3 0 CARDINAL cana-4515 149 4 0 CARDINAL cana-4515 149 5 βˆ’1 DATE cana-4515 149 6 βˆ’1 DATE cana-4515 149 7 0 CARDINAL cana-4515 151 1 2.2 CARDINAL cana-4515 152 1 2𝑛 CARDINAL cana-4515 152 2 2 CARDINAL cana-4515 152 3 1074 CARDINAL cana-4515 152 4 32 CARDINAL cana-4515 153 1 9s CARDINAL cana-4515 153 2 2295 CARDINAL cana-4515 155 1 100 CARDINAL cana-4515 158 1 1 CARDINAL cana-4515 158 2 1 CARDINAL cana-4515 158 3 2Γ—2 CARDINAL cana-4515 159 1 1 50 CARDINAL cana-4515 159 2 60 CARDINAL cana-4515 159 3 100 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2π‘˜+1)βˆ—(2π‘˜+1 CARDINAL cana-4515 185 1 2 CARDINAL cana-4515 188 1 0 CARDINAL cana-4515 188 2 0 CARDINAL cana-4515 188 3 5 CARDINAL cana-4515 188 4 5 CARDINAL cana-4515 188 5 βˆ’1 DATE cana-4515 188 6 βˆ’1 DATE cana-4515 188 7 0 CARDINAL cana-4515 188 8 βˆ’1 DATE cana-4515 188 9 βˆ’1 DATE cana-4515 189 1 2π‘˜+2)βˆ—(2π‘˜+2 CARDINAL cana-4515 192 1 5 CARDINAL cana-4515 192 2 5 CARDINAL cana-4515 192 3 βˆ’1 DATE cana-4515 192 4 βˆ’1 DATE cana-4515 192 5 0 CARDINAL cana-4515 192 6 0 CARDINAL cana-4515 192 7 βˆ’1 DATE cana-4515 192 8 5 CARDINAL cana-4515 192 9 0 CARDINAL cana-4515 194 1 2π‘˜+2)βˆ—(2π‘˜+2 CARDINAL cana-4515 195 1 0 CARDINAL cana-4515 195 2 5 CARDINAL cana-4515 195 3 5 CARDINAL cana-4515 195 4 βˆ’1 DATE cana-4515 195 5 βˆ’1 DATE cana-4515 195 6 0 CARDINAL cana-4515 195 7 βˆ’1 DATE cana-4515 195 8 5 CARDINAL cana-4515 197 1 2π‘˜+2)βˆ—(2π‘˜+2 CARDINAL cana-4515 198 1 4 CARDINAL cana-4515 200 1 0 CARDINAL cana-4515 200 2 5 CARDINAL cana-4515 200 3 βˆ’1 DATE cana-4515 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CARDINAL cana-4515 220 6 0 CARDINAL cana-4515 220 7 βˆ’1 DATE cana-4515 220 8 5 CARDINAL cana-4515 220 9 0 CARDINAL cana-4515 222 1 1074 CARDINAL cana-4515 222 2 32 CARDINAL cana-4515 223 1 9s CARDINAL cana-4515 223 2 2025 DATE cana-4515 223 3 2297 CARDINAL cana-4515 227 1 0 CARDINAL cana-4515 227 2 5 CARDINAL cana-4515 227 3 5 CARDINAL cana-4515 227 4 βˆ’1 DATE cana-4515 227 5 βˆ’1 DATE cana-4515 227 6 0 CARDINAL cana-4515 227 7 βˆ’1 DATE cana-4515 227 8 5 CARDINAL cana-4515 229 1 2π‘˜+2)βˆ—(2π‘˜+2 CARDINAL cana-4515 230 1 4 CARDINAL cana-4515 232 1 0 CARDINAL cana-4515 232 2 5 CARDINAL cana-4515 232 3 βˆ’1 DATE cana-4515 232 4 βˆ’1 DATE cana-4515 232 5 0 CARDINAL cana-4515 232 6 0 CARDINAL cana-4515 232 7 βˆ’1 DATE cana-4515 232 8 5 CARDINAL cana-4515 232 9 5 CARDINAL cana-4515 232 10 0 CARDINAL cana-4515 234 1 2π‘˜+2)βˆ—(2π‘˜+2 CARDINAL cana-4515 234 2 2.3 CARDINAL cana-4515 235 1 2n CARDINAL cana-4515 235 2 2 CARDINAL cana-4515 237 1 9 CARDINAL cana-4515 240 1 1 CARDINAL cana-4515 240 2 1 CARDINAL cana-4515 240 3 2Γ—2 CARDINAL cana-4515 240 4 𝜏(𝑇(𝑃𝑛 π‘›βˆ’2 PERSON cana-4515 241 1 1 216 CARDINAL cana-4515 241 2 192 CARDINAL cana-4515 242 1 288 CARDINAL cana-4515 243 1 + 1 DATE cana-4515 243 2 dodgson PERSON cana-4515 244 1 2 CARDINAL cana-4515 244 2 1074 CARDINAL cana-4515 244 3 32 CARDINAL cana-4515 246 1 9s CARDINAL cana-4515 246 2 2298 CARDINAL cana-4515 248 1 2 CARDINAL cana-4515 252 1 0 CARDINAL cana-4515 252 2 4 β‹± β‹± QUANTITY cana-4515 252 3 4 CARDINAL cana-4515 252 4 βˆ’1 DATE cana-4515 252 5 βˆ’1 DATE cana-4515 252 6 3 CARDINAL cana-4515 252 7 βˆ’1 DATE cana-4515 252 8 0 CARDINAL cana-4515 252 9 3 βˆ’1 β‹± β‹± QUANTITY cana-4515 252 10 βˆ’1 DATE cana-4515 252 11 4 CARDINAL cana-4515 255 1 2π‘˜+5)Γ—(2π‘˜+5 CARDINAL cana-4515 256 1 1 (8π‘˜ CARDINAL cana-4515 256 2 27 + 6 DATE cana-4515 257 1 3 CARDINAL cana-4515 257 2 18 CARDINAL cana-4515 257 3 18 Γ— 8π‘˜ 8π‘˜ PERCENT cana-4515 257 4 54 + 9 DATE cana-4515 257 5 9 CARDINAL cana-4515 257 6 1 𝑆 QUANTITY cana-4515 257 7 𝐴 𝐡 𝐡𝑇 𝐢 FAC cana-4515 262 1 4 CARDINAL cana-4515 262 2 βˆ’1 DATE cana-4515 262 3 3 CARDINAL cana-4515 262 4 βˆ’1 DATE cana-4515 262 5 0 CARDINAL cana-4515 262 6 0 CARDINAL cana-4515 262 7 βˆ’1 DATE cana-4515 270 1 2 CARDINAL cana-4515 273 1 0 CARDINAL cana-4515 273 2 0 CARDINAL cana-4515 273 3 4 CARDINAL cana-4515 273 4 4 CARDINAL cana-4515 273 5 0 CARDINAL cana-4515 273 6 βˆ’1 DATE cana-4515 273 7 3 CARDINAL cana-4515 273 8 0 CARDINAL cana-4515 273 9 βˆ’1 DATE cana-4515 273 10 βˆ’1 DATE cana-4515 276 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 280 1 4 CARDINAL cana-4515 280 2 4 CARDINAL cana-4515 280 3 βˆ’1 DATE cana-4515 280 4 3 CARDINAL cana-4515 280 5 0 CARDINAL cana-4515 280 6 0 CARDINAL cana-4515 280 7 3 βˆ’1 β‹± β‹± QUANTITY cana-4515 280 8 βˆ’1 DATE cana-4515 280 9 βˆ’1 4 MONEY cana-4515 281 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 284 1 0 CARDINAL cana-4515 284 2 β‹± β‹± WORK_OF_ART cana-4515 284 3 4 CARDINAL cana-4515 284 4 0 CARDINAL cana-4515 284 5 βˆ’1 DATE cana-4515 284 6 3 CARDINAL cana-4515 284 7 0 CARDINAL cana-4515 284 8 βˆ’1 DATE cana-4515 284 9 4 CARDINAL cana-4515 289 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 293 1 0 CARDINAL cana-4515 293 2 4 CARDINAL cana-4515 293 3 βˆ’1 DATE cana-4515 293 4 3 CARDINAL cana-4515 293 5 βˆ’1 DATE cana-4515 293 6 0 CARDINAL cana-4515 293 7 3 βˆ’1 β‹± β‹± QUANTITY cana-4515 293 8 βˆ’1 DATE cana-4515 293 9 4 CARDINAL cana-4515 295 1 2π‘˜+4)βˆ—(2π‘˜+4 CARDINAL cana-4515 298 1 1 𝑆 QUANTITY cana-4515 298 2 1 CARDINAL cana-4515 301 1 4 CARDINAL cana-4515 301 2 βˆ’1 DATE cana-4515 301 3 3 CARDINAL cana-4515 301 4 βˆ’1 DATE cana-4515 301 5 0 CARDINAL cana-4515 301 6 0 CARDINAL cana-4515 301 7 βˆ’1 DATE cana-4515 303 1 2π‘š+3)Γ—(2π‘š+3 CARDINAL cana-4515 303 2 1074 CARDINAL cana-4515 303 3 32 CARDINAL cana-4515 304 1 9s CARDINAL cana-4515 304 2 2299 CARDINAL cana-4515 306 1 2 CARDINAL cana-4515 309 1 0 CARDINAL cana-4515 309 2 0 CARDINAL cana-4515 309 3 4 CARDINAL cana-4515 309 4 4 CARDINAL cana-4515 309 5 0 CARDINAL cana-4515 309 6 βˆ’1 DATE cana-4515 309 7 3 CARDINAL cana-4515 309 8 0 CARDINAL cana-4515 309 9 βˆ’1 DATE cana-4515 309 10 βˆ’1 DATE cana-4515 311 1 2π‘š+4)Γ—(2π‘š+4 CARDINAL cana-4515 316 1 4 CARDINAL cana-4515 316 2 4 CARDINAL cana-4515 316 3 βˆ’1 DATE cana-4515 316 4 3 CARDINAL cana-4515 316 5 0 CARDINAL cana-4515 316 6 0 CARDINAL cana-4515 316 7 3 βˆ’1 β‹± β‹± QUANTITY cana-4515 316 8 βˆ’1 DATE cana-4515 316 9 βˆ’1 4 MONEY cana-4515 321 1 0 CARDINAL cana-4515 321 2 β‹± β‹± WORK_OF_ART cana-4515 321 3 4 CARDINAL cana-4515 321 4 0 CARDINAL cana-4515 321 5 βˆ’1 DATE cana-4515 321 6 3 CARDINAL cana-4515 321 7 0 CARDINAL cana-4515 321 8 βˆ’1 DATE cana-4515 321 9 4 CARDINAL cana-4515 329 1 0 CARDINAL cana-4515 329 2 4 CARDINAL cana-4515 329 3 βˆ’1 DATE cana-4515 329 4 3 CARDINAL cana-4515 329 5 βˆ’1 DATE cana-4515 329 6 0 CARDINAL cana-4515 329 7 3 βˆ’1 β‹± β‹± QUANTITY cana-4515 329 8 βˆ’1 DATE cana-4515 329 9 4 CARDINAL cana-4515 332 1 1074 CARDINAL cana-4515 332 2 32 CARDINAL cana-4515 333 1 9s CARDINAL cana-4515 333 2 2300 CARDINAL cana-4515 337 1 1 CARDINAL cana-4515 337 2 c.j. colbourn GPE cana-4515 337 3 oxford university press ORG cana-4515 337 4 new york GPE cana-4515 337 5 1980 DATE cana-4515 338 1 2 CARDINAL cana-4515 338 2 w. myrvold PERSON cana-4515 338 3 k.h. cheung PERSON cana-4515 338 4 l.b. GPE cana-4515 338 5 j.e. perry PERSON cana-4515 338 6 21 DATE cana-4515 339 1 417–419, 1991 DATE cana-4515 340 1 3 CARDINAL cana-4515 340 2 f. boesch PERSON cana-4515 340 3 c. suffel PERSON cana-4515 340 4 179 CARDINAL cana-4515 341 1 155–166, 1998 DATE cana-4515 342 1 4 CARDINAL cana-4515 342 2 brown PERSON cana-4515 342 3 p. pollak PERSON cana-4515 342 4 a. roth PERSON cana-4515 342 5 67 CARDINAL cana-4515 343 1 51–66, 1996 DATE cana-4515 344 1 5 CARDINAL cana-4515 344 2 w. moon PERSON cana-4515 344 3 f. harary PERSON cana-4515 344 4 1967 DATE cana-4515 345 1 261–271 CARDINAL cana-4515 346 1 6 CARDINAL cana-4515 346 2 kirchhoff ORG cana-4515 346 3 der gleichungen PERSON cana-4515 346 4 auf welche ORG cana-4515 346 5 bei der untersuchung der PERSON cana-4515 347 1 gefΓΌhrt wird PERSON cana-4515 347 2 annalen der physik und chemie PERSON cana-4515 347 3 72 DATE cana-4515 348 1 497–508, 1847 DATE cana-4515 349 1 7 CARDINAL cana-4515 349 2 kelmans NORP cana-4515 349 3 v.m. chelnokov 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