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A clique of a graph G is a complete subgraph of G, and the clique of largest possible size is referred to as a maximum clique (which has size known as the (upper) clique ...

Given two positive integers n and k, the bipartite Kneser graph H(n,k) is the graph whose two bipartite sets of vertices represent the k-subsets and (n-k)-subsets of ...

Bonato et al. (2014, 2015) defined the burning number of a simple graph as follows. Consider a process called burning involving are discrete time steps. Each node is either ...

"The" I graph is the path graph on two vertices: P_2. An I-graph I(n,j,k) for 1<=j,k<n and j,k!=n/2 is a generalization of a generalized Petersen graph and has vertex set ...

The rank polynomial R(x,y) of a general graph G is the function defined by R(x,y)=sum_(S subset= E(G))x^(r(S))y^(s(S)), (1) where the sum is taken over all subgraphs (i.e., ...

Let G be a graph, and suppose each edge of G is independently deleted with fixed probability 0<=p<=1. Then the probability that no connected component of G is disconnected as ...

The chromatic invariant theta(G) of a connected graph G is the number of spanning trees of G that have internal activity 1 and external activity 0. For graphs other than the ...

The Condon-Shortley phase is the factor of (-1)^m that occurs in some definitions of the spherical harmonics (e.g., Arfken 1985, p. 682) to compensate for the lack of ...

Let a graph G=(V,E) be defined on vertex set V and edge set E. Then a construction sequence (or c-sequence) for G is a linear order on V union E in which each edge appears ...

The detour index omega(G) of a graph G is a graph invariant defined as half the sum of all off-diagonal matrix elements of the detour matrix of G. Unless otherwise stated, ...