diff --git a/inference-engine/src/mkldnn_plugin/mkldnn_graph_optimizer.cpp b/inference-engine/src/mkldnn_plugin/mkldnn_graph_optimizer.cpp
index 9811b683ad19e3..b298d930d6aa9f 100644
--- a/inference-engine/src/mkldnn_plugin/mkldnn_graph_optimizer.cpp
+++ b/inference-engine/src/mkldnn_plugin/mkldnn_graph_optimizer.cpp
@@ -452,7 +452,7 @@ void MKLDNNGraphOptimizer::FuseConvolutionAndZeroPoints(MKLDNNGraph &graph) {
                 return false;
 
             auto arg0 = parent0->getParentEdgesAtPort(1)[0]->getParent();
-            if (arg0->getType() == Input && arg0->isConstant()) {
+            if (arg0->getChildEdges().size() == 1 && arg0->getType() == Input && arg0->isConstant()) {
                 if (arg0->getOriginalOutputPrecisionAtPort(0) != Precision::U8)
                     return false;
 
@@ -864,7 +864,11 @@ void MKLDNNGraphOptimizer::FusePoolingAndFakeQuantize(MKLDNNGraph &graph) {
     };
 
     auto isSutableChildNode = [](MKLDNNNodePtr node) {
-        return node->getType() == FakeQuantize && node->getAlgorithm() != Algorithm::FQBinarization;
+        bool ret = node->getType() == FakeQuantize && node->getAlgorithm() != Algorithm::FQBinarization;
+        for (size_t i = 1; i < node->getParentEdges().size(); i++) {
+            ret &= node->getParentEdgesAtPort(i)[0]->getParent()->getChildEdges().size() == 1;
+        }
+        return ret;
     };
 
     for (int i = 0; i < graphNodes.size(); i++) {
@@ -1440,12 +1444,17 @@ void MKLDNNGraphOptimizer::FuseBroadcastAndEltwise(MKLDNNGraph &graph) {
     std::vector<MKLDNNNodePtr>& graphNodes = graph.GetNodes();
 
     for (auto &graphNode : graphNodes) {
-        if (graphNode->getType() != Generic
-                || graphNode->getTypeStr() != "Broadcast"
+        if (graphNode->getType() != Broadcast
                 || graphNode->getChildEdges().size() != 1lu
                 || graphNode->getChildEdgeAt(0)->getChild()->getType() != Eltwise)
             continue;
 
+        bool ret = true;
+        for (size_t i = 1; i < graphNode->getParentEdges().size(); i++) {
+            ret &= graphNode->getParentEdgesAtPort(i)[0]->getParent()->getChildEdges().size() == 1;
+        }
+        if (!ret) continue;
+
         MKLDNNNodePtr& broadcastNode = graphNode;
         MKLDNNNodePtr eltwiseNode = broadcastNode->getChildEdgeAt(0)->getChild();
         eltwiseNode->inDims[broadcastNode->getChildEdgeAt(0)->getOutputNum()]
diff --git a/inference-engine/src/mkldnn_plugin/mkldnn_node.cpp b/inference-engine/src/mkldnn_plugin/mkldnn_node.cpp
index e46c7a7b0bdf9e..771fcb39d090c1 100644
--- a/inference-engine/src/mkldnn_plugin/mkldnn_node.cpp
+++ b/inference-engine/src/mkldnn_plugin/mkldnn_node.cpp
@@ -1328,7 +1328,7 @@ bool MKLDNNNode::canBePerformedAsScaleShift(const MKLDNNNode *parentNode) const
             if (i == fusingPort)
                 continue;
             auto weightShape = getParentEdgeAt(i)->getDims().ToSizeVector();
-            if (!isPerTensorOrPerChannelBroadcastable(dataShape, weightShape))
+            if (getParentEdgesAtPort(i)[0]->getParent()->getChildEdges().size() != 1 || !isPerTensorOrPerChannelBroadcastable(dataShape, weightShape))
                 return false;
         }
         return true;
@@ -1351,7 +1351,11 @@ bool MKLDNNNode::canBePerformedAsScaleShift(const MKLDNNNode *parentNode) const
 
 bool MKLDNNNode::canFuseSimpleOperation(const MKLDNNNodePtr& node) const {
     if (node->getType() == FakeQuantize) {
-        return node->getAlgorithm() != FQBinarization;
+        bool ret = node->getAlgorithm() != FQBinarization;
+        for (size_t i = 1; i < node->getParentEdges().size(); i++) {
+            ret &= node->getParentEdgesAtPort(i)[0]->getParent()->getChildEdges().size() == 1;
+        }
+        return ret;
     } else if (node->getType() == Eltwise) {
         return one_of(node->getAlgorithm(), EltwiseRelu, EltwiseGelu, EltwiseElu, EltwiseSigmoid, EltwiseClamp, EltwiseTanh,
                                             EltwiseSwish, EltwiseHswish, EltwiseMish, EltwiseHsigmoid, EltwiseRoundHalfToEven,
diff --git a/inference-engine/src/mkldnn_plugin/nodes/mkldnn_bin_conv_node.cpp b/inference-engine/src/mkldnn_plugin/nodes/mkldnn_bin_conv_node.cpp
index 517066d6f32806..9066b263a82035 100644
--- a/inference-engine/src/mkldnn_plugin/nodes/mkldnn_bin_conv_node.cpp
+++ b/inference-engine/src/mkldnn_plugin/nodes/mkldnn_bin_conv_node.cpp
@@ -1093,7 +1093,11 @@ bool MKLDNNBinaryConvolutionNode::canFuse(const MKLDNNNodePtr& node) const {
         return false;
 
     if (node->getType() == FakeQuantize) {
-        return node->getAlgorithm() == FQBinarization;
+        bool ret = node->getAlgorithm() == FQBinarization;
+        for (size_t i = 1; i < node->getParentEdges().size(); i++) {
+            ret &= node->getParentEdgesAtPort(i)[0]->getParent()->getChildEdges().size() == 1;
+        }
+        return ret;
     } else {
         return canFuseSimpleOperation(node);
     }
diff --git a/inference-engine/src/mkldnn_plugin/nodes/mkldnn_conv_node.cpp b/inference-engine/src/mkldnn_plugin/nodes/mkldnn_conv_node.cpp
index 36de12e94d938c..f73140065587df 100644
--- a/inference-engine/src/mkldnn_plugin/nodes/mkldnn_conv_node.cpp
+++ b/inference-engine/src/mkldnn_plugin/nodes/mkldnn_conv_node.cpp
@@ -229,7 +229,8 @@ void MKLDNNConvolutionNode::getSupportedDescriptors() {
     }
 
     if (getParentEdges().size() != expectedInputEdgesNum)
-        IE_THROW() << "Incorrect number of input edges for layer " << getName();
+        IE_THROW() << "Incorrect number of input edges for layer " << getName() << ", expected: " << expectedInputEdgesNum
+                   << " actual: " << getParentEdges().size();
     if (getChildEdges().empty())
         IE_THROW() << "Incorrect number of output edges for layer " << getName();