the first zagreb index, $m_1(g)$, and second zagreb index, $m_2(g)$, of the graph $g$ is defined as $m_{1}(g)=sum_{vin v(g)}d^{2}(v)$ and $m_{2}(g)=sum_{e=uvin e(g)}d(u)d(v),$ where $d(u)$ denotes the degree of vertex $u$. in this paper, the firstand second maximum values of the first and second zagreb indicesin the class of all $n-$vertex tetracyclic graphs are presented.

for two normal edge-transitive cayley graphs on groups h and k which have no common direct factor and gcd(jh=h ′j; jz(k)j) = 1 = gcd(jk=k ′j; jz(h)j), we consider four standard products of them and it is proved that only tensor product of factors can be normal edge-transitive.

A graph is called supermagic if there is a labeling of edges where the edges are labeled with consecutive distinct positive integers such that the sum of the labels of all edges incident with any vertex is constant. A graph G is called degree-magic if there is a labeling of the edges by integers 1, 2, ..., |E(G)| such that the sum of the labels of the edges incident with any vertex v is equal t...

In $1994,$ degree distance  of a graph was introduced by Dobrynin, Kochetova and Gutman. And Gutman proposed the Gutman index of a graph in $1994.$ In this paper, we introduce the concepts of  multiplicative version of degree distance and the multiplicative version of Gutman index of a graph. We find the sharp upper bound for the  multiplicative version of degree distance and multiplicative ver...

A set S of vertices in a graph G=(V,E) is a dominating set ofG if every vertex of V-S is adjacent to some vertex of S.For an integer k≥1, a set S of vertices is a k-step dominating set if any vertex of $G$ is at distance k from somevertex of S. In this paper, using membership values of vertices and edges in fuzzy graphs, we introduce the concepts of strength of strongestdominating set as well a...

in this paper we investigate the green‎ ‎graphs for the regular and inverse semigroups by considering the‎ ‎green classes of them‎. ‎and by using the properties of these‎ ‎semigroups‎, ‎we prove that all of the five green graphs for the‎ ‎inverse semigroups are isomorphic complete graphs‎, ‎while this‎ ‎doesn't hold for the regular semigroups‎. ‎in other words‎, ‎we prove‎ ‎that in a regular se...

matroids are important combinatorial structures and connect close-lywith graphs. matroids and graphs were all generalized to fuzzysetting respectively. this paper tries to study  connections betweenfuzzy matroids and fuzzy graphs. for a given fuzzy graph, we firstinduce a sequence of matroids  from a sequence of crisp graph, i.e.,cuts of the fuzzy graph. a fuzzy matroid, named graph fuzzy matro...