Basic graph definitions

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·^»“‡¡ˆjŠj…¼œ‡7Ž&¹`’“‰{š V …—ŽD’Žj‡ŠD(¦·9‡7𛑓‡7Ž&¹?l_½"’“œ3”‡˜Y‡–X‡¡‰QŠ_“ V …¼ŽD’ŸV(V,
t‰t“ˆ3š›‡ˆj‡7š{ {’“…Yˆ {u, v} ™OU“ˆ
Žj“–X‡ u, v ∈ V l‹¾²“ˆb‡gUmˆj–e’(˜—˜—Œ“™
…—Žc’ simple graph ≡ ∀e ∈ E, ∃u, v ∈ V, u 6= v ’“‰{š e = {u, v} .
(V, E)
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(¦»“‡ˆ^Šb…—œ¡‡Žf’(‰xš V …¼Žc’XŽj‡Šc(¦‡št‘“‡Žli½Ä’mœ3”‡˜Y‡–X‡¡‰QŠ( V …—Žc’“‰“ˆ3𛇡ˆb(V,
‡š{’(…—ˆ (u, v) ™›UmˆgŽ^m–X‡
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…¼Žc’ directed graph ≡ ∀e ∈ E, ∃u, v ∈ V u 6= v ’“‰{š e = (u, v) .
(V, E)
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Šjˆb…—t˜Y‡¡Š (V, E, w) º”t‡ˆj‡m™(…—‰’“štš›…YŠj…—“‰pŠb V ’(‰{š E ™Q“‰t‡”{’mŽi’c·9ºd‡¡…—‘“”QЦUt‰{œŠj…—“‰,¹ w : E −→ N l
Ï …—»“‡¡‰’(‰‡7𛑓‡ e ∈ E ™ w (e) º…—˜Y˜GÐx‡œ’(˜—˜Y‡7š…YŠbŽ–t˜YŠj…—t˜Y…¼œ…YŠ9Œ“l
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êxë¡ì?íSîVï3ëð V ñRòOó ë ó¡ô ë?ð E õ
²á V = {a, b, c, d, e} ™ E = {{a, c} , {b, c} , {b, d} , {c, d}}
á V = {f, g, h, i} ™ E = {(f, g) , (g, i) , (h, i)}
á
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k, l, m, n} E = {{j, k} , {j, n} ,{k, l} ,{k, m} {l, m} {m, n}}
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{o, p, q, r, s} E = {(o, p) (p, q) (p, r) (q, r) (r, p) (r, s) (s, o)}
`á V = {t,
™ E = {{t} ™ {t, u} ™ {t, v} ™ {u, v}}
Dá V = {x,u,y,v}
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z} E = {(x, y) (y, y) (z, y) (z, z)}
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á w ({k, m}) = 3 ™ w ({j, k}) = 2 ™ w ({j, n}) = w ({k, l}) = w ({m, n}) = 1
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2 w (p, q) = 1 w (p, r) = 1 w (q, r) = 1 w (r, p) = 2
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deg (v) =
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{u, v} ∈ E}| + 2
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deg (v) =
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w ({u, v}) .
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deg− (v) = |{u ∈ V | (u, v) ∈ E}| .
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X
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deg (v) =
w (u, v) .
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deg+ (v) = |{u ∈ V | (v, u) ∈ E}| .
× ‰Šj”t‡œ’“Žj‡“/’eš›…—ˆb‡œ?Šb‡š–`t˜YŠj…Yž¢‘“ˆ3’(t”
™›m‰t‡š›‡Ôx‰t‡Ž
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X
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deg (v) =
w (v, u) .
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