This paper proves the reconstruction conjecture for graphs which are isomorphic to the cube of a tree. The proof uses the reconstructibility of trees from their peripheral vertex deleted subgraphs. The main result follows from (i) characterization of the cube of a tree (ii) recognizability of the cube of a tree (iii) uniqueness of tree as a cube root of a graph G, except when G is a complete gr...

In this article, we show that the algorithm proposed by Karnopp and Rosenberg for converting a circuit into a bond graph is not fully adapted to the bond graph formalism. This formalism implicitly deletes information which is useless for describing the circuits' functioning. But this information is not systematically deleted in the bond graphs obtained with their algorithm. We propose an algori...

Let k ≥ 3 be an integer, and let G be a graph of order n with n ≥ 9k + 3− 4 √ 2(k − 1)2 + 2. Then a spanning subgraph F of G is called a k-factor if dF (x) = k for each x ∈ V (G). A fractional k-factor is a way of assigning weights to the edges of a graph G (with all weights between 0 and 1) such that for each vertex the sum of the weights of the edges incident with that vertex is k. A graph G ...

Objectives: To find the connected restrained detour number for standard graphs and mesh graphs. Methods: By determining set with minimum cardinality, of a graph is investigated. Findings: We study that altered when we add pendent vertices. The maximum degree vertices are deleted computed. Novelty: Finding path plays vital role in network-based systems. Planning largest route essential business,...

Let G be a mixed graph and L(G) be the Laplacian matrix of G. In this paper, the coefficients of the Laplacian characteristic polynomial of G are studied. The first derivative of the characteristic polynomial of L(G) is explicitly expressed by means of Laplacian characteristic polynomials of its edge deleted subgraphs. As a consequence, it is shown that the Laplacian characteristic polynomial o...

Let G be a graph of order n, and let k ≥ 2 and m ≥ 0 be two integers. Let h : E(G) → [0, 1] be a function. If ∑ e∋x h(e) = k holds for each x ∈ V (G), then we call G[Fh] a fractional k-factor of G with indicator function h where Fh = {e ∈ E(G) : h(e) > 0}. A graph G is called a fractional (k,m)-deleted graph if there exists a fractional k-factor G[Fh] of G with indicator function h such that h(...

We study the distribution of ages in mean field forest fire model introduced by Ráth and Tóth. This is an evolving random graph whose dynamics combine Erdős–Rényi edge-addition with a Poisson rain lightning strikes. All edges connected component are deleted when any its vertices struck lightning. consider asymptotic regime rates for which displays self-organized criticality. The age vertex incr...

We present a specialised constraint for enforcing graph connectivity. It is assumed that we have a square symmetrical array A of 0/1 constrained integer variables representing potential undirected edges in a simple graph, such that variable A[u, v] corresponds to the undirected edge (u, v). A search process is then at liberty to select and reject edges. The connectivity constraint ensures that ...