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1.853  Articles
1 of 186 pages  |  10  records  |  more records»
For simple connected graphs that are neither paths nor cycles, we define l(G)=max{m : G has a divalent path of length m that is not both of length 2 and in a K3}, where a divalent path is a path whose internal vertices have d... see more

Among bipartite graphs with given order and matching number/vertex cover number/edge cover number/independence number, among multipartite graphs with given order, and among graphs with given order and chromatic number, we present the graphs having the max... see more

The non-commuting graph G(G) of a non-abelian group G is defined as follows. The vertex set V(G(G)) of ?(G) is G \ Z(G) where Z(G) denotes the center of G and two vertices x and y are adjacent if and only if xy ? yx. We prove that the rainbow k-connectivi... see more

Let G be a connected graph with vertex set V(G). The Harary index of a graph is defined as H(G) = ?u ? v 1/d(u, v), where d(u, v) denotes the distance between u and v. In this paper, we determine the extremal graphs with the maximum Harary index among all... see more

A graph is an apex graph if it contains a vertex whose deletion leaves a planar graph. The family of apex graphs is minor-closed and so it is characterized by a finite list of minor-minimal non-members. The long-standing problem of determining this f... see more

The notion of the matrix Jacobson graph was introduced in 2019. Let R be a commutative ring and J(R) be the Jacobson radical of ring R. The matrix Jacobson graph of ring R size m × n, denoted ??(R)m × n, is def... see more

In graph theory, the term critical is usually used with respect to specified graph parameter P and applies when the graph G under consideration has the property P but alteration of G (such as vertex deletion, edge deletion or edge addition) result in a g... see more

We obtain the conditional fault-diameter of the square torus interconnection network under the condition of forbidden faulty sets (i.e. assuming that each non-faulty processor has at least one non-faulty neighbor). We show that under this condition, the s... see more

The signless Laplacian Estrada index of a graph G is defined as SLEE(G) = ?ni = 1eqi where q1, q2, …, qn are the eigenvalues of the signless Laplacian matrix of G. Following the previous work in which we have identified the unique graphs with maximum sign... see more

1 of 186 pages  |  10  records  |  more records»