جستجوی مقالات مرتبط با کلیدواژه « گراف » در نشریات گروه « ریاضی »

A weak odd dominating set in a graph is a subset B of vertices for which there exists a distinct set of vertices C such that every vertex in B has an odd number of neighbors in C. κ(G) denotes the size of the largest weak odd dominating set and κ'(G) the size of the smallest non weak odd dominating set. One of main motivation for studying the weak odd dominating set is their role in the design of graph-based quantum secret sharing protocols. Graph G of order n corresponds to a secret sharing protocol whose threshold is κ_Q (G)=max(κ(G),n- κ'(G)). In this paper we prove a lower bound for the largest weak odd dominating set in trees proving a conjecture for trees. Also, we present an upper bound for the largest weak odd dominating set in trees in terms of the order and the number of leaves and we improve some previous bounds.

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The current study aims to establish a connection between graphs and automata theory, which apparently demonstrate different mathematical structures. Through searching out some properties of one of these structures, we try to find some new properties of the other structure as well. This will result in obtaining some unknown properties. At first, a novel automaton called zero-forcing (Z-F) finite automata is defined according to the notion of a zero-forcing set of a graph. It is shown that for a given graph and for some zero forcing sets, various Z-F-finite automata will be obtained. In addition, the language and the closure properties of Z-F-finite automata, in particular; union, connection, and serial connection are studied. Moreover, considering some properties of graphs such as the closed trail, connected and complete; some new features for Z-F-finite automata are presented. Further, it is shown that there is not any finite graph such that f be a part of the language of its Z-F-finite automata. Actually, it is proved that for every given graph, the Z-F-finite automata of it does not show any closed trail containing all edges for every zero forcing set, but if the graph G has been a closed trail containing all edges, then the Z-F-finite automata of it has a weak closed trail containing all edges. Some examples are also given to clarify these new notions.

The fiirst leap Zagreb index of a graph, is the sum of squares of the second degrees of vertices (number of their second neighbors), and the second leap Zagreb index is the sum of the products of the second degrees of pairs of adjacent vertices, and the third leap Zagreb index is the sum of the product of the degree and second degree of the vertices.

The distinguishing number $D(G)$ of a graph $G$ is the least integer $d$ such that $G$ has an vertex labeling with $d$ labels that is preserved only by a trivial automorphism. The minimum size of a label class in such a labeling of $G$ with $D(G) = d$ is called the cost of $d$-distinguishing $G$ and is denoted by $rho_d(G)$. A set of vertices $Ssubseteq V(G)$ is a determining set for $G$ if every automorphism of $G$ is uniquely determined by its action on $S$. The determining number of $G$, ${rm Det}(G)$, is the minimum cardinality of determining sets of $G$. In this paper we compute the cost and the determining number for the friendship graphs and corona product of two graphs.

Let G be a simple graph with vertices v_1,..., v_n. The adjacency matrix of G denoted by A(G) is an n×n matrix whose the entry (i,j) is 1 if v_i and v_j are adjacent and is zero otherwise. By the eigenvalues of G we mean the eigenvalues of A(G). Let λ_1 (G)≥λ_2 (G)≥⋯≥λ_n (G) be the eigenvalues of G. In this paper we obtain some results related to graphs with at most three non-negative eigenvalues. We obtain all non-connected graphs with this property. In addition, we find some families of connected graphs with this property. In particular we study two following families of graphs:1. Graphs such as G with exactly two positive eigenvalues and one zero eigenvalues. In other words graphs such as G with λ_1 (G)>0 , λ_2 (G)>0 , λ_3 (G)=0 and λ_4 (G)0 , λ_2 (G)>0 , λ_3 (G)>0 and λ_4 (G)

To a simple graph $G=(V,E)$, we correspond a simple graph $G_{triangle,square}$ whose vertex set is ${{x,y}: x,yin V}$ and two vertices ${x,y},{z,w}in G_{triangle,square}$ are adjacent if and only if ${x,z},{x,w},{y,z},{y,w}in Vcup E$. The graph $G_{triangle,square}$ is called the $(triangle,square)$-edge graph of the graph $G$. In this paper, our ultimate goal is to provide a link between the connectedness of $G$ and $G_{triangle,square}$.

Graph theory has an important role in the area of applications of networks and clusteringý. ýIn the case of dealing with uncertain dataý, ýwe must utilize ambiguous data such as fuzzy valueý, ýfuzzy interval value or values of fuzzy numberý. ýIn this studyý, ývalues of fuzzy number were usedý. ýInitiallyý, ýwe utilized the fuzzy number value fuzzy relation and then proposed fuzzy number-value fuzzy graph on nodes and arcsý. ýIn this studyý, ýsome properties of the graph on fuzzy number-value fuzzy graph were examinedý. ýFirstý, ýwe define the Cartesian productý, ýcompositioný, ýunion and join operators on fuzzy number-value fuzzy graphs and then prove some of their properties and and give some examples for every one of definitionsý. ýWe also introduced the notion of homomorphismý, ýweak isomorphism,weak co-isomorphismý, ýisomorphismý, ýcompleteý, ýweak complete and compliment on the fuzzy number fuzzy graphs and prove some of their properties and also present some examples for every one of them.