For a simple finite graph G, the generalized adjacency matrix is defined as Aα(G)=αD(G)+(1−α)A(G),α∈[0,1], where A(G) and D(G) are respectively diagonal of vertex degrees. The Aα-spread G difference between largest eigenvalue smallest Aα(G). In this paper, we answer question posed in (Lin, Z.; Miao, L.; Guo, S. Bounds on graph. Electron. J. Linear Algebra 2020, 36, 214–227). Furthermore, show t...

We consider the real three-dimensional Euclidean Jordan algebra associated to a strongly regular graph. Then, the Krein parameters of a strongly regular graph are generalized and some generalized Krein admissibility conditions are deduced. Furthermore, we establish some relations between the classical Krein parameters and the generalized Krein parameters.

The odd graph Ok has the subsets with k elements of a set {1, . . . , 2k + 1} as its vertices set, and there exists an edge between two vertices if the corresponding pair of k-subsets is disjoint. A conjecture claims that Ok is hamiltonian for k > 2 and another long-standing conjecture implies that all odd graphs have a hamiltonian path. We proved that the prism over Ok is hamiltonian and that ...

A graph G is a chordal-k-generalized split graph if G is chordal and there is a clique Q in G such that every connected component in G[V \ Q] has at most k vertices. Thus, chordal-1-generalized split graphs are exactly the split graphs. We characterize chordal-k-generalized split graphs by forbidden induced subgraphs. Moreover, we characterize a very special case of chordal-2-generalized split ...

In the geodetic convexity, a set of vertices S graph G is convex if all belonging to any shortest path between two lie in . The hull H ( ) smallest containing If = V ), then cardinality h minimum number complementary prism GḠ arises from disjoint union and Ḡ by adding edges perfect matching corresponding A autoconnected both are connected. Motivated previous work, we study for prisms graphs. Wh...

We develop a procedure for the integration of balance equations in terms displacements orthotropic bodies with certain restrictions imposed on elastic moduli material. The components vector are expressed two functions, one which satisfies equation second order, while fourth-order equation. An algorithm is proposed solving boundary-value problems an rectangular prism. based separation principal ...

ÐIn object prototype learning and similar tasks, median computation is an important technique for capturing the essential information of a given set of patterns. In this paper, we extend the median concept to the domain of graphs. In terms of graph distance, we introduce the novel concepts of set median and generalized median of a set of graphs. We study properties of both types of median graph...

The complementary prism of a graph Γ is the ΓΓ̄, which formed from union and its complement Γ̄ by adding an edge between each pair identical vertices in Γ̄. Vertex-transitive self-complementary graphs provide vertex-transitive prisms. It was recently proved author that ΓΓ̄ core, i.e. all endomorphisms are automorphisms, whenever vertex-transitive, self-complementary, either core or complete graph. ...

‎In this paper‎, ‎we investigate the number of 1-factors of a‎ ‎generalized Petersen graph $P(N,k)$ and get a lower bound for the‎ ‎number of 1-factors of $P(N,k)$ as $k$ is odd‎, ‎which shows that the‎ ‎number of 1-factors of $P(N,k)$ is exponential in this case and‎ ‎confirms a conjecture due to Lovász and Plummer (Ann‎. ‎New York Acad‎. ‎Sci‎. ‎576(2006)‎, ‎no‎. ‎1‎, ‎389-398).

The notions of hypertree width and generalized hypertree width were introduced by Gottlob, Leone, and Scarcello in order to extend the concept of hypergraph acyclicity. These notions were further generalized by Grohe and Marx who introduced the fractional hypertree width of a hypergraph. All these width parameters on hypergraphs are useful for extending tractability of many problems in database...