Enumeration of Triangles in Quartic Residue Graphs
نویسنده
چکیده
For a fixed prime p ≡ 1 (mod 4), we define the corresponding quartic residue graph and determine the number of triangles contained in such a graph. Our computation requires us to compute the number of pairs of consecutive quartic residues modulo p via the evaluation of certain quartic Jacobi sums.
منابع مشابه
Graphs of Permutation Groups
1. Dejter, I., Giudici, R.E.: On Unitary Cayley graphs, JCMCC, 18,121-124. 2. Brrizbitia, P and Giudici, R.E. 1996, Counting pure k-cycles in sequence of Cayley graphs, Discrete math., 149, 11-18. 3. Madhavi, L and Maheswari, B.2009, Enumeration of Triangles and Hamilton Cycles in Quadratic residue Cayley graphas, Chamchuri Journal of Mathematics, 1,95-103. 4. Madhavi, L and Maheswari, B. 2010,...
متن کاملOn Tensor Product of Graphs, Girth and Triangles
The purpose of this paper is to obtain a necessary and sufficient condition for the tensor product of two or more graphs to be connected, bipartite or eulerian. Also, we present a characterization of the duplicate graph $G 1 K_2$ to be unicyclic. Finally, the girth and the formula for computing the number of triangles in the tensor product of graphs are worked out.
متن کاملQuartic Graphs with Every Edge in a Triangle
We characterise the quartic (i.e. 4-regular) multigraphs with the property that every edge lies in a triangle. The main result is that such graphs are either squares of cycles, line multigraphs of cubic multigraphs, or are obtained from the line multigraphs of cubic multigraphs by a number of simple subgraph-replacement operations. A corollary of this is that a simple quartic graph with every e...
متن کاملA CHARACTERIZATION FOR METRIC TWO-DIMENSIONAL GRAPHS AND THEIR ENUMERATION
The textit{metric dimension} of a connected graph $G$ is the minimum number of vertices in a subset $B$ of $G$ such that all other vertices are uniquely determined by their distances to the vertices in $B$. In this case, $B$ is called a textit{metric basis} for $G$. The textit{basic distance} of a metric two dimensional graph $G$ is the distance between the elements of $B$. Givi...
متن کاملHereditary biclique-Helly graphs: recognition and maximal biclique enumeration
A biclique is a set of vertices that induce a bipartite complete graph. A graph G is biclique-Helly when its family of maximal bicliques satisfies the Helly property. If every induced subgraph of G is also biclique-Helly, then G is hereditary biclique-Helly. A graph is C4-dominated when every cycle of length 4 contains a vertex that is dominated by the vertex of the cycle that is not adjacent t...
متن کامل