Let $G = (V, E)$ be a simple graph of order $n$. The total dominating set is a subset $D$ of $V$ that every vertex of $V$ is adjacent to some vertices of $D$. The total domination number of $G$ is equal to minimum cardinality of total dominating set in $G$ and denoted by $gamma_t(G)$. The total domination polynomial of $G$ is the polynomial $D_t(G,x)=sum d_t(G,i)$, where $d_t(G,i)$ is the numbe...

This paper introduces a generalization of the Tutte polynomial [14] that is defined for signed graphs. A signed graph is a graph whose edges are each labelled with a sign (+l or 1). The generalized polynomial will be denoted Q[G] = Q[G](A, B, d). Here G is the signed graph, and the letters A, B, d denote three independent polynomial variables. The polynomial Q[G] can be specialized to the Tutte...

in static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. in this paper, the static scheduling problem of automated guided vehicles in container terminal is solved by the network simplex algorithm (nsa). the algorithm is based on graph model and their performances are at least 100 times faster than traditional si...

The work of Robertson and Seymour implies that the disjoint paths problem is polynomial solvable for a fixed number of terminals. Even, Itai and Shamir showed that a weighted version of the problem is NP-hard even for a demand graph consisting of two edges. In the present paper, it is shown that the weighted disjoint paths problem is polynomial solvable for graphs embedded on a fixed surface an...

A graph is well-covered if all its maximal independent sets are of the same cardinality. Deciding whether a given graph is well-covered is known to be NP-hard in general, and solvable in polynomial time, if the input is restricted to certain families of graphs. We present here a simple structural characterization of well-covered graphs and then apply it to the recognition problem. Apparently, p...

In [4] Kauffman and Vogel constructed a rigid vertex regular isotopy invariant for unoriented four-valent graphs embedded in three dimensional space. It assigns to each embedded graph G a polynomial, denoted [G], in three variables, A, B and a, satisfying the skein relations: [ ] = A[ ] + B[ ] + [ ] [ ] = a[ ], [ ] = a[ ] and is defined in terms of a state-sum and the Dubrovnik polynomial for l...

We prove that the ribbon graph polynomial of a embedded in an orientable surface is irreducible if and only neither disjoint union nor join graphs. This result analogous to fact Tutte connected non-separable.