In this paper we investigate the dominating- -color number،  of a graph G. That is the maximum number of color classes that are also dominating when G is colored using colors. We show that where is the join of G and H. This result allows us to construct classes of graphs such that and thus provide some information regarding two questions raised in [1] and [2].  

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.

We introduce H -join decompositions of graphs, indexed by a fixed bipartite graph H . These decompositions are based on a graph operation that we call H -join, which adds edges between two given graphs by taking partitions of their two vertex sets, identifying the classes of the partitions with vertices of H , and connecting classes by the pattern H . H -join decompositions are related to modul...

In this paper we survey the behavior of various graph operations on the graph parameters clique-width and NLC-width. We give upper and lower bounds for the clique-width and NLC-width of the modi ed graphs in terms of the clique-width and NLC-width of the involved graphs. Therefor we consider the binary graph operations join, co-join, sum, di erence, products, corona, substitution, and 1-sum, an...

Bandelt, H.-J. and H.M. Mulder, Pseudo-median graphs are join spaces, Discrete Mathematics 109 (1992) 13-26. Median graphs are known to share a number of geometrica! properties with Euclidean space, as is testified by the fact that median graphs ale (c!osed) join spaces-the segments of the associated join space being the geodesic intervals of the graph. As is shown in this paper the median join...

Kulli and Muddebihal [V.R. Kulli, M.H. Muddebihal, Characterization of join graphs with crossing number zero, Far East J. Appl. Math. 5 (2001) 87–97] gave the characterization of all pairs of graphs which join product is planar graph. The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. There are only few results concerning crossing numb...

let $g$ be a connected graph. the multiplicative zagreb eccentricity indices of $g$ are defined respectively as ${bf pi}_1^*(g)=prod_{vin v(g)}varepsilon_g^2(v)$ and ${bf pi}_2^*(g)=prod_{uvin e(g)}varepsilon_g(u)varepsilon_g(v)$, where $varepsilon_g(v)$ is the eccentricity of vertex $v$ in graph $g$ and $varepsilon_g^2(v)=(varepsilon_g(v))^2$. in this paper, we present some bounds of the multi...

The crossing number cr(G) of a graph G is the minimal number of crossings over all drawings of G in the plane. Only few results concerning crossing numbers of graphs obtained as join product of two graphs are known. There was collected the exact values of crossing numbers for join of all graphs of at most four vertices and of several graphs of order five with paths and cycles. We extend these r...

We develop several algorithms taking advantage of two common approaches for bounding MPE queries in graphical models: minibucket elimination and message-passing updates for linear programming relaxations. Both methods are quite similar, and offer useful perspectives for the other; our hybrid approaches attempt to balance the advantages of each. We demonstrate the power of our hybrid algorithms ...

Structural join has been established as a primitive technique for matching the binary containment pattern, specifically the parent–child and ancestor–descendant relationship, on the tree XML data. While current indexing approaches and evaluation algorithms proposed for the structural join operation assume the tree-structured data model, the presence of reference links in XML documents may rende...