Gavril [GA4] defined two new families of intersection graphs: the interval-filament graphs and the subtree-filament graphs. The complements of intervalfilament graphs are the cointerval mixed graphs and the complements of subtree-filament graphs are the cochordal mixed graphs. The family of interval-filament graphs contains the families of cocomparability, polygon-circle, circle and chordal gra...

For a graph G=(V,E), we call subset S?V?E total mixed dominating set of G if each element V?E is either adjacent or incident to an S, and the domination number minimum cardinality G. In this paper, initiate study connected by giving some tight bounds in terms parameters such as order numbers its line graph. Then discuss on relation between diameter. Study trees 2-corona graphs our next work. Al...

We describe the missing class of the hierarchy of mixed unit interval graphs, generated by the intersection graphs of closed, open and one type of half-open intervals of the real line. This class lies strictly between unit interval graphs and mixed unit interval graphs. We give a complete characterization of this new class, as well as quadratic-time algorithms that recognize graphs from this cl...

A well-known fundamental problem in extremal graph theory is the degree/diameter problem, which is to determine the largest (in terms of the number of vertices) graphs or digraphs or mixed graphs of given maximum degree, respectively, maximum outdegree, respectively, mixed degree; and given diameter. General upper bounds, called Moore bounds, exist for the largest possible order of such graphs,...

We introduce the fast-mixed search model, which is a combination of the fast search model and the mixed search model. We establish relations between the fast-mixed search problem and other graph search problems. We also establish relations between the fast-mixed search problem and the inducedpath cover problem. We present linear-time algorithms for computing the fast-mixed search number and opt...

Mixed almost Moore graphs appear in the context of the Degree/Diameter problem as a class of extremal mixed graphs, in the sense that their order is one less than the Moore bound for mixed graphs. The problem of their existence has been considered before for directed graphs and undirected ones, but not for the mixed case, which is a kind of generalization. In this paper we give some necessary c...