The prism over a graph $G$ is the Cartesian product of with complete $K_2$. prism-hamiltonian if has Hamilton cycle. A good even cactus connected in which every block either an edge or cycle and vertex contained at most two blocks. It known that cacti are prism-hamiltonian. Indeed, showing existence spanning become common technique proving prism-hamiltonicity. Špacapan [S. Špacapan. counterexam...

Let k be a positive integer. A graph G = (V,E) is said to be Πk connected if for any given edge subset F of E(G) with |F | = k, the subgraph induced by F is connected. In this paper, we explore the minimality conditions on Πkconnectedness of a graph and also its properties of prism and corona graphs are obtained.

We determine the number of perfect matchings and forests in a family Tr,3 of triangulated prism graphs. These results show that the extremal number of perfect matchings in a planar graph with n vertices is bounded below by Ω ( 6 √ 7 + √ 37 n) = Ω (1.535) and the extremal number of forests contained in a planar graph with n vertices is bounded below by

The second Zagreb coindex is a well-known graph invariant defined as the total degree product of all non-adjacent vertex pairs in a graph. The second Zagreb eccentricity coindex is defined analogously to the second Zagreb coindex by replacing the vertex degrees with the vertex eccentricities. In this paper, we present exact expressions or sharp lower bounds for the second Zagreb eccentricity co...

In this paper, we use the concept of graph convergence of H(.,.)-co-accretive mapping introduced by [R. Ahmad, M. Akram, M. Dilshad, Graph convergence for the H(.,.)-co-accretive mapping with an application, Bull. Malays. Math. Sci. Soc., doi: 10.1007/s40840-014-0103-z, 2014$] and define an over-relaxed proximal point method to obtain the solution of a generalized variational inclusion problem ...

let $r$ be a commutative ring with identity and $m$ an $r$-module. in this paper, we associate a graph to $m$, say ${gamma}({}_{r}m)$, such that when $m=r$, ${gamma}({}_{r}m)$ coincide with the zero-divisor graph of $r$. many well-known results by d.f. anderson and p.s. livingston have been generalized for ${gamma}({}_{r}m)$. we show that ${gamma}({}_{r}m)$ is connected with ${diam}({gamma}({}_...

‎The Narumi-Katayama index was the first topological index defined‎ ‎by the product of some graph theoretical quantities‎. ‎Let $G$ be a ‎simple graph with vertex set $V = {v_1,ldots‎, ‎v_n }$ and $d(v)$ be‎ ‎the degree of vertex $v$ in the graph $G$‎. ‎The Narumi-Katayama ‎index is defined as $NK(G) = prod_{vin V}d(v)$‎. ‎In this paper,‎ ‎the Narumi-Katayama index is generalized using a $n$-ve...

We propose a new approach for defining and searching clusters in graphs that represent real technological or transaction networks. In contrast to the standard way of finding dense parts graph, we concentrate on structure edges between clusters, as it is motivated by some earlier observations, e.g. networks ecology economics applications discrete tomography. Mathematically special colorings chro...

In this article, some interesting applications of generalized inverses in the graph theory are revisited. Interesting properties employed to make proof several known results simpler, and techniques such as bordering method inverse complemented matrix methods used obtain simple expressions for Moore-Penrose incidence Laplacian matrix. Some simpler obtained special cases tree graph, complete bipa...