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     researchgate.net

     • A non-trivial graph consists of one or more vertices (or nodes) connected by edges. Each edge connects exactly two vertices, although any given vertex need not be connected by an edge. The degree of a vertex is the number of edges connected to that vertex.
     brilliant.org › wiki › graph-theory

     Graph Theory | Brilliant Math & Science Wiki

2. Top results related to what is a non-trivial graph in science meaning

   • What is a non-trivial constructor in C++?

     Top Answer

     Answered Oct 10, 2010 · 104 votes

     In simple words a "trivial" special member function literally means a member function that does its job in a very straightforward manner. The "straightforward manner" means different thing for different kinds of special member functions.

     For a default constructor and destructor being "trivial" means literally "do nothing at all". For copy-constructor and copy-assignment operator, being "trivial" means literally "be equivalent to simple raw memory copying" (like copy with memcpy).

     If you define a constructor yourself, it is considered non-trivial, even if it doesn't do anything, so a trivial constructor must be implicitly defined by the compiler.

     In order for a special member function to satisfy the above requirements, the class must have a very simplistic structure, it must not require any hidden initializations when an object is being created or destroyed, or any hidden additional internal manipulations when it is being copied.

     For example, if class has virtual functions, it will require some extra hidden initializations when objects of this class are being created (initialize virtual method table and such), so the constructor for this class will not qualify as trivial.

     For another example, if a class has virtual base classes, then each object of this class might contain hidden pointers that point to other parts of the very same object. Such a self-referential object cannot be copied by a simple raw memory copy routine (like memcpy). Extra manipulations will be necessary to properly re-initialize the hidden pointers in the copy. For this reason the copy constructor and copy-assignment operator for this class will not qualify as trivial.

     For obvious reasons, this requirement is recursive: all subobjects of the class (bases and non-static members) must also have trivial constructors.

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     1/5

   • What is a minimal path in a graph?

     Top Answer

     Answered Nov 15, 2008 · 6 votes

     Minimal path is the set of edges which when traversed cover the least amount of distance between two edges. Minimal distance is the sum of the distance between the edges of a minimal path.

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     2/5

   • What is the meaning of a DIR File and what is exactly a DDF In EMV ICC file structure?

     Top Answer

     Answered Jan 27, 2022 · 1 votes

     Can someone please explain to me what is a Directory in ICC.

     EMV card file structure is based on ISO/IEC 7816-4. You better read it first. There you can find detailed description of many terms you are talking about. Generally, there are two types of card files: DF (dedicated file) and EF (elementary file). EF cantains binary data. DF can contain any file. Every file (both DF and EF) can be selected with APDU SELECT. Every selected file can send as a response FCI structure -- data with general information about this file (type, size, attributes and so on).

     what is the difference between a DDF and its related DIR

     EMV book 1: "The DIR file is an AEF (in other words, an EF) with a record structure according to this specification including the following data objects according to ISO/IEC 7816-4. ..."

     DDF and ADF are subtypes of DF. An ADF is the entry point to one or more Application Elementary Files (AEFs). A DDF is an entry point to other ADFs or DDFs.

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     3/5

   • What is the meaning of "rendezvous" in computer science?

     Top Answer

     Answered Sep 17, 2011 · 3 votes

     Maybe you mean that: http://en.wikipedia.org/wiki/Synchronous_rendezvous ?

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     4/5

   • In a random graph: What is the probability that a node has a link to any node on a list x defined special nodes?

     Top Answer

     Answered Apr 05, 2016 · 4 votes

     For a non-special node, there are x potential edges from that node to a special node. For any such potential edge the probability of the edge not being in the graph is 1-p. Assuming independence, the probability that it avoids all special nodes is (1-p)^x. The complementary probability is what you seek, it is

     1 - (1-p)^x-

     For special nodes, the probability that a given special node is connected to one of the other special nodes is

     1 - (1-p)^(x-1)-

     You can combine these answers in various ways. Pick a node at random. The probability that it is either special or has an edge connecting it to a special node is:

     x/N + (N-x)/N * [1-(1-p)^x]-

     the probability that it has an edge connecting to a special node is:

     x/N * [1 - (1-p)^(x-1)] + (N-x)/N * [1 - (1-p)^x]-

     in all cases -- these tend to 1 as x tends to N.

     Since this is Stack Overflow, a bit of programming is in order. Here is a Python 3 Monte Carlo simulation that seems to suggest the accuracy of the formula for the probability that a randomly selected node is either special or adjacent to a special:

     import random-#The following function returns a random graph on nodes#0,1,...,N-1 where edges are chosen with probability p#The graph is returned as a dictionary keyed by the #The corresponding values are sorted lists of adjacent nodesdef randGraph(N,p): #initialize G: G = {} for i in range(N): G[i] = [] #iterate through potential edges: for i in range(N-1): for j in range(i+1,N): if random.random() < p: G[i].append(j) G[j].append(i) #sort adjacency lists before returning: for i in G: G[i].sort() return G#A function to determine the number of nodes#in a graph that are either#special or connected to a special,#where special means: 0,1,2,...,xdef specialsAndFriends(G,x): count = 0 for i in G: if (i<x) or (len(G[i]) > 0 and G[i][0] < x): count +=1 return count#now -- a Monte Carlo simulation:def estimateProb(N,p,x,trials = 1000): estimates = [] for i in range(trials): G = randGraph(N,p) estimates.append(specialsAndFriends(G,x)/N) return sum(estimates)/trials#compare with:def exactProb(N,p,x): return x/N + (N-x)/N * (1 - (1-p)**x)

     (Python 2 would need to adjust e.g. x/N to float(x)/N).

     Sample output:

     >>> estimateProb(100,0.25,10)0.9496800000000086>>> >>> exactProb(100,0.25,10)0.9493178367614746

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3. math.stackexchange.com · questions · 1364996terminology - What is a nontrivial graph? - Mathematics Stack ...

   math.stackexchange.com · questions · 1364996

   

   Jul 17, 2015 · I use empty graph to mean a graph without edges, and therefore a nonempty graph would be a graph with at least one edge. According to both wikipedia.com and wikibooks.com, a trivial graph is a graph with 1 vertex and 0 edges.

4. People also ask

   What is a non-trivial graph?

   • A non-trivial graph consists of one or more vertices (or nodes) connected by edges. Each edge connects exactly two vertices, although any given vertex need not be connected by an edge. The degree of a vertex is the number of edges connected to that vertex. In the graph below, vertex A A is of degree 3, while vertices B B and C C are of degree 2.

   Graph Theory | Brilliant Math & Science Wiki

   brilliant.org/wiki/graph-theory/

   See all results for this question

   What is the difference between a trivial graph and a nonempty graph?

   • @ManuelLafond I agree. I use empty graph to mean a graph without edges, and therefore a nonempty graph would be a graph with at least one edge. According to both wikipedia.com and wikibooks.com, a trivial graph is a graph with 1 vertex and 0 edges.

   What is a nontrivial graph? - Mathematics Stack Exchange

   math.stackexchange.com/questions/1364996/what-is-a-nontrivial-graph

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   What is a trivial graph?

   • 3. Trivial Graph: A graph is said to be trivial if a finite graph contains only one vertex and no edge. A trivial graph is a graph with only one vertex and no edges. It is also known as a singleton graph or a single vertex graph. A trivial graph is the simplest type of graph and is often used as a starting point for building more complex graphs.

   Types of Graphs with Examples - GeeksforGeeks

   www.geeksforgeeks.org/graph-types-and-applications/

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   What is a non-trivial connected graph?

   • This graph meets the definition of connected vacuously (since an edge requires two vertices). A non-trivial connected graph is any connected graph that isn't this graph. A non-trivial connected component is a connected component that isn't the trivial graph, which is another way of say that it isn't an isolated point.

   terminology - What is a Non-Trivial Connected Graph? - Mathematics

   math.stackexchange.com/questions/2080962/what-is-a-non-trivial-connected-graph

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5. www.geeksforgeeks.org · graph-types-and-applicationsTypes of Graphs with Examples - GeeksforGeeks

   www.geeksforgeeks.org · graph-types-and-applications

   

   • Finite Graphs. A graph is said to be finite if it has a finite number of vertices and a finite number of edges. A finite graph is a graph with a finite number of vertices and edges.
   • Infinite Graph: A graph is said to be infinite if it has an infinite number of vertices as well as an infinite number of edges.
   • Trivial Graph: A graph is said to be trivial if a finite graph contains only one vertex and no edge. A trivial graph is a graph with only one vertex and no edges.
   • Simple Graph: A simple graph is a graph that does not contain more than one edge between the pair of vertices. A simple railway track connecting different cities is an example of a simple graph.

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7. brilliant.org · wiki · graph-theoryGraph Theory | Brilliant Math & Science Wiki

   brilliant.org · wiki · graph-theory

   

   Terminology. A non-trivial graph consists of one or more vertices (or nodes) connected by edges. Each edge connects exactly two vertices, although any given vertex need not be connected by an edge. The degree of a vertex is the number of edges connected to that vertex.

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9. math.stackexchange.com · questions · 2080962terminology - What is a Non-Trivial Connected Graph ...

   math.stackexchange.com · questions · 2080962

   

   Jan 2, 2017 · The trivial graph is the graph on one vertex. This graph meets the definition of connected vacuously (since an edge requires two vertices). A non-trivial connected graph is any connected graph that isn't this graph.

10. en.wikipedia.org · wiki · Strongly_connected_componentStrongly connected component - Wikipedia

    en.wikipedia.org · wiki · Strongly_connected_component

    

    Definitions. A directed graph is called strongly connected if there is a path in each direction between each pair of vertices of the graph. That is, a path exists from the first vertex in the pair to the second, and another path exists from the second vertex to the first.

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12. www.cs.columbia.edu · ~cs4203 · filesOutline 1.1 Graphs and Digraphs 1.2 Common Families of Graphs ...

    www.cs.columbia.edu · ~cs4203 · files

    

    Proposition 1.1. A non-trivial simple graph G must have at least one pair of vertices whose degrees are equal. Proof. pigeonhole principle Theorem 1.2 (Euler’s Degree-Sum Thm). The sum of the degrees of the vertices of a graph is twice the number of edges. Corollary 1.3. In a graph, the number of vertices having odd degree is an even number.

13. www.math.kit.edu · iag6 · lehreLecture Notes Graph Theory - KIT

    www.math.kit.edu · iag6 · lehre

    

    The graph Gis non-trivial if it contains at least one edge, i.e., E 6= ;. non-trivial Equivalently, Gis non-trivial if Gis not an empty graph. The order of G, denoted by jGj, is the number of vertices of G, i.e., jGj= jVj. order, jGj