
A connected graph
In this paper, we prove two conjectures of Baca concerning
Some special sum graphs and difference graphs, based on abelian groups, are discussed. In addition to Li’s result on character sum estimates, Weil’s character sum estimates are also used to show that these are indeed Ramanujan graphs.
A critical set in a Latin square of order
We study combinatorial structure of
It is proved in this paper that for any integer
Employing trading signed design algorithm, we construct an automorphism-free
Consider those graphs
We enumerate the 2-
A
The following partition problem was first introduced by R.C. Entringer and has subsequently been studied by the first author and more recently by Bollobas and Scott, who consider the hypergraph version as well, using a probabilistic technique. The partition problem is that of coloring the vertex set of a graph with
In a communication network, several vulnerability measures are used to determine the resistance of the network to disruption of operation after the failure of certain stations or communication links. If we think of a graph as modeling a network, the edge-integrity of a graph is one \textbf{measure of graph vulnerability} and it is defined to be the minimum sum of the orders of a set of edges being removed and a largest remaining component. In this paper, the edge-integrity of graphs
In this paper, it is shown that the necessary condition for the existence of a holey perfect Mendelsohn design (HPMD) with block size 5, type
The computational complexity of the graph isomorphism problem is still unknown. We consider Cartesian products
Tenacity is a recently introduced parameter to measure vulnerability of networks and graphs. We characterize graphs having the maximum number of edges among all graphs with a given number of vertices and tenacity.
In this paper, we show that some graphs are circuit unique by applying a new tool, which is the character of the matching polynomial. Some properties of the character of the matching polynomial is also given.
The theory of hypergeometric functions is brought to bear on a problem—namely, that of obtaining a certain power series expansion involving the sine function that is inclusive of the Catalan sequence and which serves as a prelude to the calculation of other related series of similar type. A general formulation provides the particular result of interest as a special case, into which Catalan numbers are introduced as desired.
A splitting partition for a graph
A decomposition of a digraph is said to be bicyclic if it admits an automorphism consisting of exactly two disjoint cycles. Necessary and sufficient conditions are given for the existence of bicyclic decompositions of the complete digraph into each of the four orientations of a 4-cycle.
The integrity of a graph
for all
If the distance between two vertices
It is shown that for every pair
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