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The Randić spectral radius rho_(Randic) of a graph is defined as the largest eigenvalue of its Randić matrix.

A simple graph is a line graph of some simple graph iff if does not contain any of the above nine graphs, known in this work as Beineke graphs, as a forbidden induced ...

There are several related theorems involving Hamiltonian cycles of graphs that are associated with Pósa. Let G be a simple graph with n graph vertices. 1. If, for every k in ...

A maximal independent vertex set of a graph is an independent vertex set that cannot be expanded to another independent vertex set by addition of any vertex in the graph. A ...

Combinatorics is the branch of mathematics studying the enumeration, combination, and permutation of sets of elements and the mathematical relations that characterize their ...

De Grey (2018) found the first examples of unit-distance graphs with chromatic number 5, thus demonstrating that the solution to the Hadwiger-Nelson problem (i.e., the ...

An ordered pair (a,b) of nonnegative integers such that there is some set of a points and b edges whose removal disconnects the graph and there is no set of a-1 nodes and b ...

Every graph with n vertices and maximum vertex degree Delta(G)<=k is (k+1)-colorable with all color classes of size |_n/(k+1)_| or [n/(k+1)], where |_x_| is the floor ...

Let v(G) be the number of vertices in a graph G and h(G) the length of the maximum cycle in G. Then the shortness exponent of a class of graphs G is defined by sigma(G)=lim ...

The lower clique number omega_L(G) of a graph G may be defined as the size of a smallest maximal clique in a graph G. It therefore corresponds to the coefficient of the ...