Struct Graph 

pub struct Graph { /* private fields */ }

A graph represented as an adjacency list

Implementations

impl Graph

pub fn new(n: usize) -> Self

Create a new empty graph with n vertices

pub fn add_edge(&mut self, u: usize, v: usize) -> Result<(), &'static str>

Add an edge between vertices u and v

pub fn degree(&self, v: usize) -> Result<usize, &'static str>

Get the degree of a vertex

pub fn first_zagreb_index(&self) -> usize

Calculate the first Zagreb index of the graph

pub fn min_degree(&self) -> usize

Get the minimum degree of the graph

pub fn max_degree(&self) -> usize

Get the maximum degree of the graph

pub fn is_k_connected(&self, k: usize, use_exact: bool) -> bool

Check if the graph is k-connected (wrapper function)

Arguments

• k - The connectivity parameter to check
• use_exact - Whether to use the exact algorithm (slower but more accurate) or the approximation

Returns

true if the graph is k-connected, false otherwise

pub fn is_k_connected_approx(&self, k: usize) -> bool

Check if the graph is k-connected using an approximation algorithm This is faster but may give incorrect results in some cases

pub fn is_k_connected_exact(&self, k: usize) -> bool

Check if the graph is k-connected using an exact algorithm based on Menger’s theorem This is slower but gives correct results for all graphs

pub fn independence_number_approx(&self) -> usize

Calculate independence number (approximate) Finding the exact independence number is NP-hard, so this is a greedy approximation

pub fn is_likely_hamiltonian(&self, use_exact_connectivity: bool) -> bool

Check if the graph is likely Hamiltonian using Theorem 1 from the paper and known graph properties

Arguments

• use_exact_connectivity - Whether to use exact connectivity checking (slower but more accurate)

pub fn is_likely_traceable(&self, use_exact_connectivity: bool) -> bool

Check if the graph is likely traceable using Theorem 2 from the paper and known graph properties

Arguments

• use_exact_connectivity - Whether to use exact connectivity checking (slower but more accurate)

pub fn zagreb_upper_bound(&self) -> f64

Calculate upper bound on Zagreb index using Theorem 3 from the paper

pub fn vertex_count(&self) -> usize

Get the number of vertices

pub fn edge_count(&self) -> usize

Get the number of edges

Trait Implementations

impl Clone for Graph

fn clone(&self) -> Graph

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for Graph

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.