
Figueroa-Centeno, Ichishima, and Muntaner-Batle [3, 4] proved some results on felicitous graphs and raised the following conjectures:
In this paper, the conjectures are partially settled by proving the following results:
In this paper, we characterize the graphs
This note will complete the computation of all Ramsey numbers
For a graph
Any
The Hosoya index of a graph is defined as the summation of the coefficients of the matching polynomial of a graph. In this paper, we give an explicit expression of the Hosoya index for the graphs
Let
The Laplacian eigenvalues of linear phenylenes
The notion of equitable coloring was introduced by Meyer in 1973. This paper presents exact values of the equitable chromatic number of three corona graphs, which include the complete graph and its complement
A construction of graphs, codes, and designs acted on by simple primitive groups described in [9, 10] is used to find some self-orthogonal, irreducible, and indecomposable codes acted on by one of the simple Janko groups,
Let
A set
In this paper, we determine
For given finite simple graphs
A
Determining whether or not a graph has an efficient dominating set (equivalently, a perfect code) is an NP-complete problem. Here we present a polynomial time algorithm to decide if a given simplicial graph has an efficient dominating set. However, the efficient domination number decision problem is NP-complete for simplicial graphs.
The purpose of this note is to give two binomial sums with generalized Fibonacci sequences. These results generalize two binomial sums by Kilic and Ionascu in The Fibonacci Quarterly, 48.2(2010), 161-167.
Let
In this paper we prove that every planar graph without
A new construction of authentication codes with arbitration using singular pseudo-symplectic geometry on finite fields is given. Some parameters and the probabilities of success for different types of deceptions are computed.
Two graphs are defined to be adjointly equivalent if their complements are chromatically equivalent. By
In this paper, we discuss the properties of a class of generalized harmonic numbers
We prove that
A family
Open Problem [11]: Let
In this paper, we extend this study to an infinite class of convex polytopes obtained as a combination of the graph of an antiprism
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