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Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer?.

Solutions for Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE. Download more important topics, notes, lectures and mock test series for GATE Exam by signing up for free.

Here you can find the meaning of Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Let G = (V, E ) be a directed, weighted graph with weight function w : E → R. For some function f : V → R, for each edge (u , v ) ∈ E, define w ′(u , v ) as w (u , v ) + f (v ).Which one of the options completes the following sentence so that it is TRUE?“The shortest paths in G under w are shortest paths under w′ too, ________”.a)If and only if f (u) is the distance from s to u in the graph obtained by adding a new vertex s to G and edges of zero weight from s to every vertex of Gb)If and only if ∀u ∈ V , f (u ) is positivec)If and only if ∀u ∈ V , f (u ) is negatived)For every f : V → RCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.