Let G be an undirected graph with vertex and edge sets V (G) E(G), respectively. A set S ⊆ is called a hop independent dominating of if both G. The minimum cardinality G, denoted by γhih(G), the domination number In this paper, we show that lies between independence We characterize these types in shadow graph, join, corona, lexicographic product two graphs. Moreover, either exact values or boun...

In the graph distance game, two players alternate in constructing a maximal path. The objective function is the distance between the two endpoints of the path, which one player tries to maximize and the other tries to minimize. In this paper we examine the distance game for various graph operations: the join, the corona and the lexicographic product of graphs. We provide general bounds and exac...

In this paper we introduce a new graph composition, called 2-amalgam, and we prove that the 2-amalgam of perfect graphs is perfect. This composition generalizes many of the operations known to preserve perfection, such as the clique identification, substitution, join and amalgam operations. We give polynominal-time algorithms to determined whether a general graph is decomposable with respect to...

In this paper, we explore the design of algorithms for the problem of checking whether an undirected graph contains a negative cost cycle (UNCCD). It is known that this problem is significantly harder than the corresponding problem in directed graphs. Current approaches for solving this problem involve reducing it to either the b-matching problem or the T -join problem. The latter approach is m...

We investigate the problem of optimizing distributed queries by using semijoins in order to minimize the amount of data communication between sites. The problem is reduced to that of finding an optimal semijoin sequence that locally fully reduces the relations referenced in a general query graph before processing the join operations. The optimization of general queries, in a distributed databas...

We introduce joins of signed graphs and explore the chromatic number all-positive all-negative joins. prove an analogue to theorem that join two equals sum their numbers. Given graphs, is usually less than numbers, by amount depends on new concept deficiency a signed-graph coloration.

Worst-case optimal join algorithms are the class of join algorithms whose runtime match the worst-case output size of a given join query. While the first provably worse-case optimal join algorithm was discovered relatively recently, the techniques and results surrounding these algorithms grow out of decades of research from a wide range of areas, intimately connecting graph theory, algorithms, ...

In 2020 Bang-Jensen et. al. generalized the Haj\'os join of two graphs to class digraphs and several results for vertex colorings in digraphs. Although, as a consequence these results, digraph can be obtained by constructions (directed identifying non-adjacent vertices), determining obtain is complex problem. particular, et posed problem operations construct symmetric 5-cycle from complete orde...

Let G be a simple, connected graph and let A(G) the adjacency matrix of G. If D(G) is diagonal vertex degrees G, then for every real $$\alpha \in [0,1]$$ , $$A_{\alpha }(G)$$ defined as }(G) = \alpha + (1- ) A(G).$$ The eigenvalues form }$$ -spectrum $$G_1 {\dot{\vee }} G_2$$ {\underline{\vee \langle \text {v} \rangle {e} denote subdivision-vertex join, subdivision-edge R-vertex join R-edge two...

A counterexample is presented to the following conjecture of Jackson and Wormald: If j ~ 1, k ~ 2 and a graph is connected, locally jconnected and K l , (j+l)(k-l)+2 -free then it has a k-tree. Preliminaries All graphs considered here are finite and without loops or multiple edges. As usual, we let V(G) and E(G) denote respectively the vertex set and the edge set of the graph G. The cardinality...