By combining the notions of interval-valued m-polar fuzzy graphs and graphs, notion cubic is first introduced. Then, degree a vertex in complete defined. After that, concepts direct product strong are given. Moreover, weak isomorphism co-weak defined, examples given to prove that not an isomorphism. Finally, complement presented.

Characterisations of interval graphs, comparability graphs, co-comparability graphs, permutation graphs, and split graphs in terms of linear orderings of the vertex set are presented. As an application, it is proved that interval graphs, cocomparability graphs, AT-free graphs, and split graphs have bandwidth bounded by their maximum degree.

the vertex-edge wiener index of a simple connected graph g is defined as the sum of distances between vertices and edges of g. two possible distances d_1(u,e|g) and d_2(u,e|g) between a vertex u and an edge e of g were considered in the literature and according to them, the corresponding vertex-edge wiener indices w_{ve_1}(g) and w_{ve_2}(g) were introduced. in this paper, we present exact form...

let g be a simple graph with vertex set v(g) {v1,v2 ,...vn} . for every vertex i v , ( ) i  vrepresents the degree of vertex i v . the h-th order of randić index, h r is defined as the sumof terms1 2 11( ), ( )... ( ) i i ih  v  v  vover all paths of length h contained (as sub graphs) in g . inthis paper , some bounds for higher randić index and a method for computing the higherrandic ind...

‎let $g$ be a graph with vertex set $v(g)$ and edge set $x(g)$ and consider the set $a={0,1}$‎. ‎a mapping $l:v(g)longrightarrow a$ is called binary vertex labeling of $g$ and $l(v)$ is called the label of the vertex $v$ under $l$‎. ‎in this paper we introduce a new kind of graph energy for the binary labeled graph‎, ‎the labeled graph energy $e_{l}(g)$‎. ‎it depends on the underlying graph $g$...

Let $A$ and $B$ be two disjoint subsets of the vertex set $V$ of a graph $G$. The set $A$ is said to dominate $B$, denoted by $A rightarrow B$, if for every vertex $u in B$ there exists a vertex $v in A$ such that $uv in E(G)$. For any graph $G$, a partition $pi = {V_1,$ $V_2,$ $ldots,$ $V_p}$ of the vertex set $V$ is an textit{upper domatic partition} if $V_i rightarrow V_j$ or $V_j rightarrow...

Hoàng defined the P4-sparse graphs as the graphs where every set of five vertices induces at most one P4. These graphs attracted considerable attention in connection with the P4-structure of graphs and the fact that P4-sparse graphs have bounded clique-width. Fouquet and Giakoumakis generalized this class to the nicely structured semi-P4-sparse graphs being the (P5, co-P5, co-chair)-free graphs...