A total coloring of a graph is an assignment of colors to all the elements (vertices and edges) of the graph such that no two adjacent or incident elements receive the same color. In this paper, we prove the tight bound of the Behzad and Vizing conjecture on total coloring for the corona product of two graphs G and H , when H is a cycle, a complete graph or a bipartite graph.

Results about wreath products of circulant graphs are used to construct infinitely many circulant graphswith efficient dominating setswhose elements need not be equally spaced in Zn. It is proved that if a circulant graph of large degree has an efficient dominating set, then either its elements are equally spaced, or the graph is the wreath product of a smaller circulant graph with an efficient...

A Set S of vertices in a graph G(V,E) is called dominating set,if every vertex v V id either an element or adjacent to S. vertice Total set if S, total G with no isolated subset the such that In this paper we will find perfect Interval graph. We also out induced subgraph regarding which were splitted.

‘Domination in graphs’ has been studied extensively and at present it is an emerging area of research in graph theory. An introduction and an extensive overview on domination in graphs and related topics is surveyed and detailed in the two books by Haynes et al. [1,2]. Product of graphs occurs naturally in discrete mathematics as tools in combinatorial constructions. They give rise to an import...

Partial cubes are defined as isometric subgraphs of hypercubes. For a partial cube G, its crossing graph G# is introduced as the graph whose vertices are the equivalence classes of the Djoković–Winkler relation Θ, two vertices being adjacent if they cross on a common cycle. It is shown that every graph is the crossing graph of some median graph and that a partial cube G is 2-connected if and on...

We prove that, for each p ≥ 1, there exists a polynomial time algorithm for finding a minimum domination set in the class of all (Kp, P5)-free graphs. Let G be a graph with vertex-set V (G) and edge-set E(G). The notation x ∼ y (respectively, x 6∼ y) means that vertices x, y ∈ V (G) are adjacent (respectively, non-adjacent). Moreover, if X ⊆ V (G) and y ∈ V (G)\X, we write y ∼ X (respectively, ...

In an edge deletion problem one is asked to delete at most k edges from a given graph such that the resulting graph satisfies a certain property. In this work, we study four NP-complete edge deletion problems where the goal graph has to be a chain, a split, a threshold, or a co-trivially perfect graph, respectively. All these four graph classes are characterized by a common forbidden induced su...

Let be a non-trivial simple graph. A dominating set in graph is of vertices such that every vertex not the adjacent to at least one set. subset minimum neighborhood if and for holds. The cardinality called as number it denoted by . where intersection neighborhoods all small possible, (i.e., ). number, , In other words, smallest needed form neighborhood-dominating concept related study structure...

X iv :0 80 9. 25 51 v1 [ m at h. C O ] 1 5 Se p 20 08 Spanning Trees in Grid Graphs Paul Raff July 25, 2008 Abstract A general method is obtained for finding recurrences involving the number of spanning trees of grid graphs, obtained by taking the graph product of an arbitrary graph and path or cycle. The results in this paper extend the work by Desjarlais and Molina and give concrete methods f...